SlideShare a Scribd company logo
1 of 60
Download to read offline
SNJ‡




    êÆÔnû!
        ±j
˜uŒÆêƉÆX9úôŒÆêƉƥ%
     ÜÜêÆØ
    ÜS, 2005c10'

       ±j   êÆÔnû!
SNJ‡


SNJ‡
 1   VØ
 2   êÆ[†êÆÔn
 3   ²YÔn†êÆ
 4   g“Ôn†êÆ
 5   y“Ôn†êÆ
                 ±j    êÆÔnû!
SNJ‡


SNJ‡
 1   VØ
 2   êÆ[†êÆÔn
 3   ²YÔn†êÆ
 4   g“Ôn†êÆ
 5   y“Ôn†êÆ
                 ±j    êÆÔnû!
SNJ‡


SNJ‡
 1   VØ
 2   êÆ[†êÆÔn
 3   ²YÔn†êÆ
 4   g“Ôn†êÆ
 5   y“Ôn†êÆ
                 ±j    êÆÔnû!
SNJ‡


SNJ‡
 1   VØ
 2   êÆ[†êÆÔn
 3   ²YÔn†êÆ
 4   g“Ôn†êÆ
 5   y“Ôn†êÆ
                 ±j    êÆÔnû!
SNJ‡


SNJ‡
 1   VØ
 2   êÆ[†êÆÔn
 3   ²YÔn†êÆ
 4   g“Ôn†êÆ
 5   y“Ôn†êÆ
                 ±j    êÆÔnû!
VØ
            êÆ[†êÆÔn
             ²;Ôn†êÆ
             C“Ôn†êÆ
             y“Ôn†êÆ
êÆÔn†nØÔn
   ôv¬§
§^=ŠJ¯µ/UÄwŠ·êÆÔn†nØÔ
   n'«yº0
   2004?a¬ïÄ)±¡xsk^=Š£‰µ/ö'8'
   ؘ$quot;0ÚzXÖ¿µ/êÆÔn6êƧ
nØ
   Ôn95Ônquot;0
 Ágµ/œ'9~ Ѓ'Ï4(2005-9-28) ))Pôv¬Ó“
 À©HmêÆïĤ0
                 ±j    êÆÔnû!
VØ
         êÆ[†êÆÔn
          ²;Ôn†êÆ
          C“Ôn†êÆ
          y“Ôn†êÆ
êÆÔn†nØÔn


  êÆ   êÆÔn ÔnÆ nØÔn g,F




              ±j    êÆÔnû!
VØ
        êÆ[†êÆÔn
         ²;Ôn†êÆ
         C“Ôn†êÆ
         y“Ôn†êÆ
Ÿo¬kêÆÔnº
  ­þ)ÃêÆÔn§‰'õ
§Òk
ù€Æ¯quot;
  êÆÚÔn)5Ñ5uég,F'@£quot;
  Œ´§‚g'uÐq22‡Ñé¢Sy–Ú¯K'ïÄ,
  UìnØSQ'quot;{¦ugduÐquot;
  ù«aF'uÐÚ‡Ñv¡w5Øv´êÆ[½ÔnÆ[g
  „gW'œåiZ§¢¢Sþ22k¿ŽØ '¢SA^quot;

             ±j    êÆÔnû!
VØ
        êÆ[†êÆÔn
         ²;Ôn†êÆ
         C“Ôn†êÆ
         y“Ôn†êÆ
Ÿo¬kêÆÔnº
  9XOê´ég,'¯œ§¢êÆ[9©uAûXe'¯
  Kµ
              x n + y n = zn

  Qn  2žvkš²…'êA(¤çŒ½n¤quot;
  ù‡¯K'@Ø)vk?Û¢S¿Âquot;
  êÆ[
Aûù‡¯KuÐ
Œ'“êêØ'nØquot;
  ùnØ'˜Ü©QyQ'OŽÅž“Q—è†cènØ¥
  åX­‡Š^quot;
             ±j     êÆÔnû!
VØ
        êÆ[†êÆÔn
         ²;Ôn†êÆ
         C“Ôn†êÆ
         y“Ôn†êÆ
Ÿo¬kêÆÔnº
  q9XlèGÿþ1¢S¯KuÐѲ¡AÛÆ£ F1¤
  Ú‡©AÛ£Gauss)quot;
  9u²¡AÛÆ¥k9²I‚'IÊú£v†‚©˜Xk
  …ak˜^²I‚¤'?Ø—
¤¢'šîAÛquot;
  ùq¢´˜‡vky¢F'Ä–?ا¢¥¡AÛÚV­
  AÛQy“¤”Eâ£XCAT×£¤þkA^quot;
   ¡¬! AÛÆQÔn¥'˜A^quot;
             ±j    êÆÔnû!
VØ
         êÆ[†êÆÔn
          ²;Ôn†êÆ
          C“Ôn†êÆ
          y“Ôn†êÆ
Ÿo¬kêÆÔnº
  ÔnÆ'ïÄ¥k‡quot;äNy–Ú¯K'nØJÑquot;
  ¢¨B© o«Ä)'Š^åµÚå§b^å§fŠ^å§
  rŠ^åquot;
  ÔnÆ[XEinstein£OÏdquot;¤J¦ùo«Š^å'˜‡
  Ú˜'nØquot;
  d¦‚‰Xˆ«}Á§Jш«nØFquot;

              ±j    êÆÔnû!
VØ
        êÆ[†êÆÔn
         ²;Ôn†êÆ
         C“Ôn†êÆ
         y“Ôn†êÆ
Ÿo¬kêÆÔnº

  µ§˜‡ÔnF´Ä¤õ'̇sO´´ÄJø
¢¨Œ
  ±¨y'ýóquot;
  ùFk'‰Ñ
ýó§¢8c'¢¨^‡„Ã{¨y§
  ùÜ©'ÔnxŒ±¡ŠnØÔn¶
  k'„?QêÆí'0㧄vk‰Ñ¢¨Œ±¨y'ý
  ó§ùÜ©'ÔnxŒ±¡ŠêÆÔnquot;

             ±j    êÆÔnû!
VØ
             êÆ[†êÆÔn
              ²;Ôn†êÆ
              C“Ôn†êÆ
              y“Ôn†êÆ
êÆ[†êÆÔn
  êÆÔn'ÑyØ´éÈ'¯œquot;
  Q²YÔnuÐ'žÏ§Ø
¢¨ÔnÆ[§ÔnÆ[Ó
  ž´êÆ[§XNewton, Lagrange, Laplace, Fourier,
  Gauss, Maxwell1quot;
  Einsteink©ÙuvQêÆD““Mathematische
  Annalen”þquot;
  êƆÔnˆg'uЦ§‚Åì©lquot;
  êÆÔn´êÆ[†ÔnÆ[ŒU¡Ó97'˜+§g
  c5Åì¹#å5quot;
                  ±j    êÆÔnû!
VØ
         êÆ[†êÆÔn
          ²;Ôn†êÆ
          C“Ôn†êÆ
          y“Ôn†êÆ
êÆ[†êÆÔn
  † g“§˜•Œ'êÆ[é97ÔnÆquot;XHilbert!
  v5êÆÔn{6§ïÄvPƒéضWeylïÄvP
  ƒéا!v5žm!˜m!ÔŸ6¶CartanïÄvPÂ
  ƒéضvon NeumannïÄvþfåÆquot;
  kêÆ[ϏêÆÔnéêÆ)kXíÄ
ïÄêÆ
  Ôn§¦‚¿vkéÐ'ÔnÔö§é¤ïÄ'é–'Ôn
  ¿ÂÚÔn폿Ø97quot;

              ±j    êÆÔnû!
VØ
        êÆ[†êÆÔn
         ²;Ôn†êÆ
         C“Ôn†êÆ
         y“Ôn†êÆ
êÆ[†êÆÔn
  êÆ[Œ±¥b'˜‡¯¢´µ¦‚Œ±UìêÆSQ'S
  ÆuÐêƧ
ØU97¦‚nØ'A^quot;
  lÔnÆ[@p'‡quot;´µØ´ÔnA^
uÐ'êÆn
  ØQÔn¥k^quot;
  ·‡'²¨´µÉÔnÆ[éu¦‚'óŠJøî‚Ä
  :'êÆóŠ,QêÆþé­‡§¢Ø‡Ï4 ÔnÆ
  ['3üÚ­Àquot;
             ±j    êÆÔnû!
VØ
           êÆ[†êÆÔn
            ²;Ôn†êÆ
            C“Ôn†êÆ
            y“Ôn†êÆ
uêÆ[†êÆÔn
  Žk)40c“–¯Princetonp1ïĤ'ž
  ÿ§EinsteinQgCú¿•¦HÚ˜|Ø'Ž{§F
  4¦ëù˜¡'ïÄquot;
  EinsteinQk)'8‡p˜cgC'©Ù§Œ´ü‡r~
  v
@©Ù„2Q@quot;
  Einstein'“Ö5JPk)µ/xoŒ±òEinstein'©
  Ù˜Q8‡p˜ƒØnQº0
  k)Ø@Einstein'Ž{k#n§vk‹‘¦‰Ú˜|
  ؐ¡'ïħ
´U‰gC'êÆïÄquot;
                ±j    êÆÔnû!
VØ
         êÆ[†êÆÔn
          ²;Ôn†êÆ
          C“Ôn†êÆ
          y“Ôn†êÆ
uêÆ[†êÆÔn

  A›cv
§k)¤uÐ'Chern-WeilnØ
  ÚChern-SimonsnØQÔn¥P'A^quot;
  
EinsteinQÚ˜|ؐ¡'ãåÄ)þ@´”}
§
  ,¦J¦Ú˜nØ'gŽ˜†ò‰
e5§¤y“nØ
  ÔnÚêÆÔn'SgŽquot;
  k•Œ¤Ò'˜½´kÌ„'œ

              ±j    êÆÔnû!
VØ
          êÆ[†êÆÔn
           ²;Ôn†êÆ
           C“Ôn†êÆ
           y“Ôn†êÆ
uêÆ[†êÆÔn
  uÛŽk)é­ÀêÆÔn'ïħ¦ïÆxÜm¦k)
  ¥s‰ÆêÆïĤ?˜?ïħonØÔnïÄ¿Ì
  ?quot;
  Üm¦k)uêxŒÆêÆX§É’uͶÚOÔnÆ[4
  V£R©H©Fowler¤§QÅ£N©Bohr¤Ú |£W.
  Pauli¤bóŠquot;
  ¦##
u¯k)!£)k)!ûˉk)!Á­k)
  1ïÄ)quot;
               ±j    êÆÔnû!
VØ
        êÆ[†êÆÔn
         ²;Ôn†êÆ
         C“Ôn†êÆ
         y“Ôn†êÆ
uêÆ[†êÆÔn

  ºék)éêÆÔnkÏ'ïħ~Xéuy¨wk
  )JÑ'S‰|؆‡©AÛéänØ'9X‰Ñv­‡ 
  zquot;
  ¦##
êÆÔnïĐ¡'˜¥jåþquot;y²
*¿
  ™5ICߎ'±•‰k)Úy²vxõߎ'4Ž¸k)
  с´¦'ïÄ)quot;

             ±j    êÆÔnû!
VØ
        êÆ[†êÆÔn
         ²;Ôn†êÆ
         C“Ôn†êÆ
         y“Ôn†êÆ
uêÆ[†êÆÔn

  #‡Ík)Qþ­V²«c“=m©†¨wk)ÜŠcI
  S‰|ؐ¡'ïħ´·sêÆÔnïÄ'mÿöƒ˜quot;
  sS„kxõÙ¦l¯êÆÔnïÄ'cêÆ[§QdØ
  U˜˜J9
quot;


             ±j    êÆÔnû!
VØ
         êÆ[†êÆÔn
          ²;Ôn†êÆ
          C“Ôn†êÆ
          y“Ôn†êÆ
uêÆ[†êÆÔn

  £¤Ðk)¼Fieldsø'ü‘óŠÑ†êÆÔnk9quot;
  ¦†SchoenAû' Ÿþߎ´PƒéØ¥'¯Kquot;
  ¦¤y²'CalabiߎQ‡unØ¥å9…Š^quot;


              ±j    êÆÔnû!
VØ
        êÆ[†êÆÔn
         ²;Ôn†êÆ
         C“Ôn†êÆ
         y“Ôn†êÆ
uêÆ[†êÆÔn

  £k)4åJ†ÚíÄêÆÔnAy´‡unØ'êÆï
  Äquot;
  Q{suêÆFk±¦'Æ)ÌN'˜I“cêÆ[ï
  ÄêÆÔnquot;
  QsS§“cÆ)éù˜+„quot;))quot;GdŬ§·Ž
  ‰˜’Dquot;

             ±j    êÆÔnû!
VØ
          êÆ[†êÆÔn
           ²;Ôn†êÆ
           C“Ôn†êÆ
           y“Ôn†êÆ
²;Ôn†êÆ

  ²YÔn¹åÆ!9åÆÚÚOåÆ!b^Æ!IÆ1
  ¡quot;
  §‚^ DÚêÆ'ØÓ©|§éù©|'MáÚuÐå
  
íÄŠ^quot;
  e¡‰˜{ãquot;

               ±j    êÆÔnû!
VØ
           êÆ[†êÆÔn
            ²;Ôn†êÆ
            C“Ôn†êÆ
            y“Ôn†êÆ
Úî(Newton)åƆ~‡©§|

   ÚîI½ÆF = maŒ!Šµ
                      d2
                 m         r = F.
                      dt 2
   ù´˜‡0~‡©§|§%dЩ ˜ÚЩ„ÝŒ
   AÑŸX?¿ž' ˜Ú„Ýquot;

                ±j       êÆÔnû!
VØ
             êÆ[†êÆÔn
              ²;Ôn†êÆ
              C“Ôn†êÆ
              y“Ôn†êÆ
kÚå
  Úî'%kÚå½ÆŒ!Šµ
             d2         Mm            GMm
         m        r = −G 3 r =    (         ).
             dt 2       |r |           |r |

  ´UþÚÄþ
                       1 ˙ 2 GMm
                  E=     mr −
                       2       |r |
                            ˙
                  L = r × mr .

  Åðquot;ddŒíÑmÊV(Kepler)n½Æquot;
                   ±j    êÆÔnû!
VØ
               êÆ[†êÆÔn
                ²;Ôn†êÆ
                C“Ôn†êÆ
                y“Ôn†êÆ
.‚KFåƆC©{
  ½Â.‚KF(Lagrange)þ
                        ˙       1 ˙     GMm
               L(r (t), r (t)) = mr 2 +
                                2        |r |

  阴»r : [t , t ] → R , ½Â.‚KFÈ©µ
           0   1
                       3


                       t1
                                     ˙
                            L(r (t), r (t))dt
                      t0




                       ±j        êÆÔnû!
VØ
           êÆ[†êÆÔn
            ²;Ôn†êÆ
            C“Ôn†êÆ
            y“Ôn†êÆ
.‚KFåƆC©{
  é.‚KFÈ©'g©ÑEuler-Lagrange§µ
               d ∂L      ∂L
                       −     = 0.
                    ˙
               dt ∂ xi   ∂xi

  ù1duÚî'%kÚ吧quot;
  g©{P¦^u‡©AÛ¥µXÿG‚!xÚN
  ì!MorsenØ1quot;

                 ±j    êÆÔnû!
VØ
                  êÆ[†êÆÔn
                   ²;Ôn†êÆ
                   C“Ôn†êÆ
                   y“Ôn†êÆ
M—îåƆquot;AÛ
  l.‚KFþŒ±½Âw—î(Hamilton)þµ
                          H :=           pi qi − L,
                                     i

                         ∂L
  where qi = xi , pi =   ∂qi ,   i = 1, 2, 3.
  åÆþvˆ¼êf (p, q)§§'6ЧŒ±!µ
                    d
                       f (p, q) = {H, f (p, q)}.
                    dt


                             ±j          êÆÔnû!
VØ
            êÆ[†êÆÔn
             ²;Ôn†êÆ
             C“Ôn†êÆ
             y“Ôn†êÆ
M—îåƆquot;AÛ
  d?{·, ·}Xe½Â'Ñt(Poisson))Òµ
                               ∂f ∂g     ∂f ∂g
          {f , g} =        (           −         ).
                               ∂qi ∂pi   ∂pi ∂qi
                      i

  w—îåÆ-u
‡©AÛÆ¥4AÛÚÑtAÛ'u
  Ðquot;
  Ï~iùAÛ¥§iùÝþ˜­0é¡Üþ§
4@¨½
  Ñt@¨­0‡¡Üþquot;
                      ±j         êÆÔnû!
VØ
        êÆ[†êÆÔn
         ²;Ôn†êÆ
         C“Ôn†êÆ
         y“Ôn†êÆ
9åÆÚÚOåÆ

  ·é„vkÆvõ£‡È©'žÿÆ9åÆ'aúPÁc
  5quot;ƒ8éõkaq'²{quot;
  ÚOåÆ|^VÇÚO'gŽd‡B6Äí÷By–§ù
  rc
VÇØÚÚOÆ'uÐquot;
  ÚOåƏþfåÆ'uЋe
gŽþ'Ä:quot;

             ±j    êÆÔnû!
VØ
         êÆ[†êÆÔn
          ²;Ôn†êÆ
          C“Ôn†êÆ
          y“Ôn†êÆ
^Ɔõ£‡È©
  b^Æ´õ£‡È©A^'IŸ‰~quot;
  ŒêÆ[Gaussë†v§'uЧQb^Æk˜‡Ônþ
  'ü ±¦·¶quot;
  b^Æ'uÐv§¥¢¨åX9…Š^§¢´ò§í IŸ
  'ºX'%´êÆ'Äquot;
  ðŽd‰(Maxwell)±¦'êÆõåò˜¢¨y–o@
  ˜êƐ§quot;
              ±j    êÆÔnû!
VØ
            êÆ[†êÆÔn
             ²;Ôn†êÆ
             C“Ôn†êÆ
             y“Ôn†êÆ
ðŽd‰§
  ðŽd‰ÄuêÆþ{'Ä '§Ð†ÔnÆ[
   '˜½ÆØΧ 5y²´ÔnÆ[á†
quot;
  ðŽd‰l¦'§‰Ñ
b^Å'ýóÚIb^Å'ß
  Ž§ 5Ñ 
¢¨y¢quot;
  e¡o‡§yQ¡ðŽd‰§µ
            · E = 4πρ,                 · H = 0,
            1 ∂H                   1 ∂H   4π
     ×E +        = 0,       ×H −        =    J.
            c ∂t                   c ∂t    c

                   ±j    êÆÔnû!
VØ
              êÆ[†êÆÔn
               ²;Ôn†êÆ
               C“Ôn†êÆ
               y“Ôn†êÆ
ðŽd‰§†^Å
  Qý˜¥§k
              1 ∂H                    1 ∂H
       ×E +        = 0,        ×H −        = 0.
              c ∂t                    c ∂t
  %k
       1 ∂E       2            1 ∂H       2
              =       E,              =       H.
       c 2 ∂t                  c 2 ∂t

  =E ÚH ÷vÅЧ, dd‰Ñb^Å'ýóquot;
                      ±j   êÆÔnû!
VØ
         êÆ[†êÆÔn
          ²;Ôn†êÆ
          C“Ôn†êÆ
          y“Ôn†êÆ
ðŽd‰§†dƒéØ
  ðŽd‰§'ïÄ',˜‡­‡@t´dƒéØquot;
  {.I(Faraday)’
ŠI'DÂ'HŸ'±'V
  gquot;
  ðŽd‰5¿ Xt±´'½'§QØÓ'ëìXeI„
  ØÓquot;
  ù†ðŽÖ(Michelson)'Ͷ¢¨ØÎquot;

              ±j    êÆÔnû!
VØ
                   êÆ[†êÆÔn
                    ²;Ôn†êÆ
                    C“Ôn†êÆ
                    y“Ôn†êÆ
ðŽd‰§†dƒéØ
  âÔ[(Lorentz)ÚOÏdquot;(Einstein) ´QdÄ:þuÐ
  
dƒéا‰Ñ
5'ž˜Bquot;
  DŒÅdÄ(Minkowski)‰Ñ'êÆAº^ ‚S“ꥂ
  Sg†'VgµžmÚ˜m¨¤˜‡o‘˜mµ
                 R4 = {(t, x, y, z) : t, x, y, z ∈ R},

  ØÓëìXƒm'‹sd‚Sg†
                    (t , x , y , z ) = (t, x, y, z)A

  ‰Ñ£A˜o0¤§¦
  −c 2 dt 2 +dx 2 +dy 2 +dz 2 = −c 2 (dt )2 +(dx )2 +(dy )2 +(dz )2 .
                            ±j     êÆÔnû!
VØ
          êÆ[†êÆÔn
           ²;Ôn†êÆ
           C“Ôn†êÆ
           y“Ôn†êÆ
ðŽd‰§†5‰|Ø

  ðŽd‰Qí¦'§ž§^ b^³'Vgquot;
  ÔnÆ[¦5±ù´˜‡êÆóä§vkÔn¿Âquot;
   5'uÐy²§b^³´Ä)'Ônþ§Ø
Q¢¨
  þk¤¢Born-Aharonov¨A§QnØþ†—S‰|
  Ø'Ñyquot;

               ±j    êÆÔnû!
VØ
          êÆ[†êÆÔn
           ²;Ôn†êÆ
           C“Ôn†êÆ
           y“Ôn†êÆ
C“Ôn†êÆ

  ·ùp`'g“Ôn'´PƒéØ!þfåÆÚS‰|
  Øquot;
  §‚^ þ˜­VkŒuÐ'xõêÆ©|µ‡©AÛ!ÿ
  ÀÆ!v«Ø1quot;


               ±j    êÆÔnû!
VØ
          êÆ[†êÆÔn
           ²;Ôn†êÆ
           C“Ôn†êÆ
           y“Ôn†êÆ
2ƒéرc‡©AÛ
     £pd¤dGGÿþ'¯KÑu§ïÄn‘˜m¥'
  Gauss
  ­¡nØquot;
  Q¦'Ä:þ§Riemann£iù¤JÑ
‡©AÛ'nØÄ
  :quot;
  éiùAÛ'ïÄ¥Ñy'Üþ©ÛQåÆïÄ¥kPA
  ^quot;
  ùž®Ñy
ChristoffelÎÒ1quot;
               ±j    êÆÔnû!
VØ
          êÆ[†êÆÔn
           ²;Ôn†êÆ
           C“Ôn†êÆ
           y“Ôn†êÆ
2ƒé؆‡©AÛ
  iùAÛ'•ŒA^´Einstein£OÏdquot;¤Má'Pƒ
  éØquot;
  PƒéØÑuX´^‘­LorentzÝþ'6G5£ãž
  ˜§Einstein§òAÛþ(Ricci­Ç¤†Ônþ£Uþ¨Ä
  þÜþ¤éXå5quot;
  êÆ[FËA(Hilbert)^g©{íÑ
ý˜¥
  'Einstein§§¢¦gC`vk=‡êÆ[Œ±“
  OEinsteinquot;
               ±j    êÆÔnû!
VØ
        êÆ[†êÆÔn
         ²;Ôn†êÆ
         C“Ôn†êÆ
         y“Ôn†êÆ
2ƒéØ¢¨yâ
  PƒéØ'k±eýóµY@Y#'cÄ!I‚'­!
  çÉ'Q!ÚåÅ11quot;
  Y@Y#'cÄQPƒéØJѱcÒB© 
quot;
  PƒéØJÑØȧu)
˜gF quot;˜‡Bÿ¢|Bÿ
   
I‚QNg'­quot;
  ¨˜‡Æ)¯¦µXtvk y¢§¦¬xo`quot;OÏd
  quot;£‰µ/@o§·ÐŠO'þPa ¢Ãquot;ÃØX
  Û§ù‡nØ´ ('quot;0
             ±j    êÆÔnû!
VØ
          êÆ[†êÆÔn
           ²;Ôn†êÆ
           C“Ôn†êÆ
           y“Ôn†êÆ
2ƒéØ¢¨yâ
  çɏkéõBÿyâquot;k'´HawkingÚPenrose^
  ‡©ÿÀÆØyçÉ'QSquot;
  PƒéØ'˜‡­‡íØ´Ä'‰»Fµ‰»´Aä
  ½Â 'quot;ùdwÇ(Hubble)'Bÿ¤|±quot;
  †dƒ9'k‰»'Œ¿åFquot;ù‡F'ýóƒ˜
  ´‰»¥QµË§ù®Bÿ 
quot;
  ÚåÅ'Bÿ´¨V˜‡­‡'‘8quot;
               ±j    êÆÔnû!
VØ
            êÆ[†êÆÔn
             ²;Ôn†êÆ
             C“Ôn†êÆ
             y“Ôn†êÆ
2ƒé؆y“‡©AÛ
  PƒéØQêÆþ'­Œ¿Â´4Œ'rc
‡©AÛ'
  uÐquot;
  CartanÚWeylс}ÁòEinstein'Úån؆Maxwell'
  b^nØÚ˜å5§d¦‚¦^
‡©AÛ¥'éän
  Øquot;
  QCartan'󊥧©‡©GªÚÌm1AÛé–uÐå5
  
§ù‡©AÛ†“êÿÀ'@Ü‹e
Ä:quot;

                 ±j    êÆÔnû!
VØ
           êÆ[†êÆÔn
            ²;Ôn†êÆ
            C“Ôn†êÆ
            y“Ôn†êÆ
Žk)†y“‡©AÛ
  Žk)¤uÐ'a'nØ´˜‡Øe'IŸºXquot;
  k)u
CartanQ‡©AÛ¥¦^©‡©Gª'DÚquot;
  ¦uÐ'^‡©Gª“v«Sa!^‡©Gª'‡Ý 
  ?«Sa(Chern-SimonsnØ!Bott-ChernV­‡Ý¤1Ñ
  ´4'gŽquot;
  QÜ•²k)'§w¥k['Hquot;

                ±j    êÆÔnû!
VØ
          êÆ[†êÆÔn
           ²;Ôn†êÆ
           C“Ôn†êÆ
           y“Ôn†êÆ
Žk)†y“‡©AÛ

  k)'óŠPK
‡©AÛ!“êAÛ!“êêØ!
  “êÿÀ1õ‡+quot;
  ¦'óŠµdµ/ÙKr9¤kêÆ+quot;0
  Ù¥c­‡'´Atiyah!Singer1uÐ'snØquot;
   ¡¬! ¦‚QÔn¥'A^quot;

               ±j    êÆÔnû!
VØ
               êÆ[†êÆÔn
                ²;Ôn†êÆ
                C“Ôn†êÆ
                y“Ôn†êÆ
Einstein   †£¤Ðk)
     †k)ØÓ
†Cartanƒaq§£¤Ðk)k)š~97
     ÔnÆquot;
     ¦¼Fieldsø'ü‘óŠÑ†Einsteink9µ˜‘´PÂ
     ƒéØ¥' Ÿþߎ§˜‘´9uKahler-EinsteinÝþ
                             ¨
     'Calabiߎquot;
     XtEinsteiné¦!{¬´Ÿo$'|µ§U¢‰·‚
     'Ž–åuž
quot;
                    ±j    êÆÔnû!
VØ
         êÆ[†êÆÔn
          ²;Ôn†êÆ
          C“Ôn†êÆ
          y“Ôn†êÆ
þfn؆VÇØ
  þ˜­VÊ›c“±c†PƒéØ|{'´þfåÆquot;
  †EinsteinA¢˜ïá
PƒéØ'nØe¨Ø
  Ó§þfåÆ´QxõÔnÆ['¡ÓãåeuÐå5'§
  Ùv§¥kxõ¹¢ÚØquot;
  ~X§QþfåÆ¥éÔŸ6Äæ^
aq9åÆ¥'VÇ
  Aºquot;
  ,Einstein)éIb¨A'Aº¦¦¤þfnØ'M
  ©ƒ˜§¦éBrown6ĉv­‡ïħ¦éù«Aº
  ±~¦Ýquot;
              ±j    êÆÔnû!
VØ
               êÆ[†êÆÔn
                ²;Ôn†êÆ
                C“Ôn†êÆ
                y“Ôn†êÆ
Einstein   †þfnØ
     D`¦éÀ`µ/J#‚ý'ƒ8þP‚•f¯
     íº0À£¹#µ/·‚ØUþPTxo‰œ0
     Einstein¨céþfåÆ'˜Ÿ¦¤
yQþf8EÆ'
     ÑuX§Qù‡+gc5k˜¢¨§X¢ï•ë†'˜
     ¢¨quot;
     ùpJ ù´
rx±eêÆÚÔn'ØÓµ¢¨´u
     ¨ÔnnØ'ªsOquot;·‚¬w vknØ'kI?
     اk¢¨Ãl‰åquot;
                    ±j    êÆÔnû!
VØ
         êÆ[†êÆÔn
          ²;Ôn†êÆ
          C“Ôn†êÆ
          y“Ôn†êÆ
þfåƆ¼©Û
  bf7X¦fØ”='FkéŒ'(JµdMaxwell'n
  اbfQ”=v§¥¬uÑb^Ë
›”Uþ§ªá
   ¦fØþquot;
  ù«Ë'ȈAT´ë‰'§Œ¢SBÿ'IÌ´lÑ
  'quot;
  þfåÆ¥'˜‡Aºdk¶'Ž™§‰Ñµ
                   ∂
               i      ψ = Hψ
                   ∂t
  d?H ˜0‡©Žfquot;
              ±j      êÆÔnû!
VØ
         êÆ[†êÆÔn
          ²;Ôn†êÆ
          C“Ôn†êÆ
          y“Ôn†êÆ
þfåƆ¼©Û

  ùžŒ±¦^ ‡©§½¼©Û'nصH 'Ì´lÑ
  '§éAXbf6Ä'U?§U?ƒm'yéAXË'
  IÌquot;
  þfåÆrc
¼©Û'uеVon Neumann1ë†
  
þfåƆ¼©Û'ïÄquot;


              ±j    êÆÔnû!
VØ
           êÆ[†êÆÔn
            ²;Ôn†êÆ
            C“Ôn†êÆ
            y“Ôn†êÆ
þfåƆ+Ø

  þfåÆ¥g”†Äþ'ïÄïá
†êÆ¥+ØÚv«
  ؃m'éXquot;
  êÆ[Weyl, Van Der WaerdenÑ!v+؆þfåƐ¡
  'Öquot;
  êÆ[Harish-Chandra¦5´ÆÔn'§dué+ØÚv«
  ØaD§=¤têÆ'quot;

                ±j    êÆÔnû!
VØ
                êÆ[†êÆÔn
                 ²;Ôn†êÆ
                 C“Ôn†êÆ
                 y“Ôn†êÆ
Dirac   §
        ldƒéØ'ŸþUþ9XŒ±ÑKlein-Gordan§quot;
        ù´˜‡0¡‡©§quot;
        duSchrodinger§¥éžm'ê´˜0'§Dirac£A
               ¨
        .Ž¤Ä
¤¢Klein-Gordan§'”²Š”§=k¶
        'Dirac§quot;
        ù‡§'ý󃘴 bf'Q§du¨ž„vkBÿ
           bf§DiracY éõ'‹§§9X5gHeisenbergquot;

                     ±j    êÆÔnû!
VØ
                 êÆ[†êÆÔn
                  ²;Ôn†êÆ
                  C“Ôn†êÆ
                  y“Ôn†êÆ
Dirac   §†InØ
        Dirac'Ž{QêÆþ´Ñ¢¿'§QsnØ¥å9
        …Š^quot;AityahÚSingeruÐ'snØ'I˜ÚÒ´‡Q
        ˜„'6Gþ¨iDiracŽfquot;
        s½nåuRiemann-RochúªÚGauss-Bonnetúª§
        QaÚ'bnØ'Ä:þ§Hirzebruchy²
p‘
        'Riemann-RochúªÚÎÒúª£Ç©dk)Qù¡
        kóŠ¤quot;
        Hirzebruch'óŠÚu
GrothendieckQù¡'󊧁
        ª—
AityahÚSingeruÐ'snاÙI˜ÚÒ´‡
        Q˜„'6Gþ¨iDiracŽfquot;
                      ±j    êÆÔnû!
VØ
               êÆ[†êÆÔn
                ²;Ôn†êÆ
                C“Ôn†êÆ
                y“Ôn†êÆ
Feynman   È©
    l²YåÆ þfåÆkü«YµlHamiltonåÆÑu§
    ^ uþfz'{Œ± Schrodinger§¶
                         ¨
    lLagrangeåÆÑu§Œ±—FeynmanÈ©quot;
    Feynman'{åuDiracÖ¥˜‡¢'remark§ÙÄ)
    é–´Ä´»˜mþ'È©quot;
    ùaÈ©êÆþ˜„vkÂ(,kWienerÿÝ'n
    ؤ§¢ÔnÆ[uÐј{§Œ±‰ÑkÔn¿Â'
    ýóquot;
                    ±j    êÆÔnû!
VØ
               êÆ[†êÆÔn
                ²;Ôn†êÆ
                C“Ôn†êÆ
                y“Ôn†êÆ
Feynman   È©

        È©QÔn¥PA^§ÔnÆ[^§Œ±
    Feynman
     êÆþ¿ŽØ '@t§¤±êÆ[@´ÔnÆ['
     Û{¥quot;
    êÆ[¤‰'22´^êƐ{y²ÔnÆ['˜ßŽ§
    
ØU
AÔnÆ[ˆ ùߎ'g´quot;


                    ±j    êÆÔnû!
VØ
          êÆ[†êÆÔn
           ²;Ôn†êÆ
           C“Ôn†êÆ
           y“Ôn†êÆ
y“nØÔnÚêÆ
  ·¤`'y“nØÔn)±Yang-MillsS‰|؏Ä:'
  þf|Ø!±Pƒé؏Ä:'þfÚånØÚ±Ú˜ù
  üöª48s'‡unØquot;
  §‚'¡ÓAX´6^
quot;5quot;õ'y“êƵ‡©AÛ!
  “êAÛ!ÿÀÆ!v«Ø11quot;
  §‚¥xõïďquot;5quot;õ'vyêÆÔn§
ØnA
  nØÔnquot;
               ±j    êÆÔnû!
VØ
          êÆ[†êÆÔn
           ²;Ôn†êÆ
           C“Ôn†êÆ
           y“Ôn†êÆ
y“nØÔnÚêÆ
  é­‡'´§duêÆÔnªÆ‰'¦^êƧ‚'ïÄr
  c
êÆ)'uÐquot;
  ~X§éS‰|Ø'ïÄ—
Donaldsonn
  Ø!Seiberg-WittennØ'Ñy§§‚Jø
DÚ'‡©ÿ
  À¤ØUJø'5'{quot;
  ­‘þfÚå'ïÄ—
“êAÛ¥Riemann¡'˜m
  'Wittenߎ'ÑyÚKontsevich 'y²quot;

               ±j    êÆÔnû!
VØ
              êÆ[†êÆÔn
               ²;Ôn†êÆ
               C“Ôn†êÆ
               y“Ôn†êÆ
‡unØ
  ‡unØq¢êÆ'Ú˜åX錊^quot;
  §r¤
vertex operator algebra, Gromov-Witten theory
  and mirror symmetry11'#)quot;
  du£¤Ðk)y²Calabiߎ
Ñy'Calabi-Yau6GQ
  ‡unØïÄ¥åØ7Š^quot;
  ‡unØ¥éóS'gŽ—
éõ-¯Û'ߎ§k
  ®²êÆ[y²
quot;
                     ±j   êÆÔnû!
VØ
           êÆ[†êÆÔn
            ²;Ôn†êÆ
            C“Ôn†êÆ
            y“Ôn†êÆ




dužm9XØU‰['Hquot;
Œ±ëoœ'Ö5‡unØüÂ6Ú·'©
Ùµ”Derivatives in Mathematics and Physics” quot;
Brian Green'Ö5‰»'Œu6£The Elegant Universe).




                 ±j   êÆÔnû!
VØ
         êÆ[†êÆÔn
          ²;Ôn†êÆ
          C“Ôn†êÆ
          y“Ôn†êÆ
(Š

 ÛÏgS§)g˜À¶
 ”
 ÛÏgS§)Ø)«¶
 ÛÏgS§)gäv¶
 ÛÏgS§)ÃÄ~¶
 ÛÏgS§U)%{quot;”
        —58yŒ“{¥²6




              ±j    êÆÔnû!

More Related Content

What's hot

Laxham Viajaya Laxham
Laxham Viajaya LaxhamLaxham Viajaya Laxham
Laxham Viajaya Laxhamguest0e4c1c
 
PMT-006-生產計劃與管理
PMT-006-生產計劃與管理PMT-006-生產計劃與管理
PMT-006-生產計劃與管理handbook
 
俄罗斯进出口标准,技术规格,法律,法规,中英文,目录编号RG 2660
俄罗斯进出口标准,技术规格,法律,法规,中英文,目录编号RG 2660俄罗斯进出口标准,技术规格,法律,法规,中英文,目录编号RG 2660
俄罗斯进出口标准,技术规格,法律,法规,中英文,目录编号RG 2660Turkmenistan Laws
 
俄罗斯进出口标准,技术规格,法律,法规,中英文,目录编号RG 2681
俄罗斯进出口标准,技术规格,法律,法规,中英文,目录编号RG 2681俄罗斯进出口标准,技术规格,法律,法规,中英文,目录编号RG 2681
俄罗斯进出口标准,技术规格,法律,法规,中英文,目录编号RG 2681Turkmenistan Laws
 
俄罗斯Gost标准,进出口购买商品目录№RG 3783
俄罗斯Gost标准,进出口购买商品目录№RG 3783俄罗斯Gost标准,进出口购买商品目录№RG 3783
俄罗斯Gost标准,进出口购买商品目录№RG 3783Turkmenistan Laws
 
俄罗斯Gost标准,进出口购买商品目录№RG 425
俄罗斯Gost标准,进出口购买商品目录№RG 425俄罗斯Gost标准,进出口购买商品目录№RG 425
俄罗斯Gost标准,进出口购买商品目录№RG 425Turkmenistan Laws
 
Telugu bible 80)_old_testament
Telugu bible 80)_old_testamentTelugu bible 80)_old_testament
Telugu bible 80)_old_testamentWorldBibles
 
俄罗斯进出口标准,技术规格,法律,法规,中英文,目录编号RG 2676
俄罗斯进出口标准,技术规格,法律,法规,中英文,目录编号RG 2676俄罗斯进出口标准,技术规格,法律,法规,中英文,目录编号RG 2676
俄罗斯进出口标准,技术规格,法律,法规,中英文,目录编号RG 2676Turkmenistan Laws
 
俄罗斯Gost标准,进出口购买商品目录№RG 3757
俄罗斯Gost标准,进出口购买商品目录№RG 3757俄罗斯Gost标准,进出口购买商品目录№RG 3757
俄罗斯Gost标准,进出口购买商品目录№RG 3757Turkmenistan Laws
 
俄罗斯Gost标准,进出口购买商品目录№RG 1306
俄罗斯Gost标准,进出口购买商品目录№RG 1306俄罗斯Gost标准,进出口购买商品目录№RG 1306
俄罗斯Gost标准,进出口购买商品目录№RG 1306Turkmenistan Laws
 
Обеспечение безопасности web приложений
Обеспечение безопасности web приложенийОбеспечение безопасности web приложений
Обеспечение безопасности web приложенийSQALab
 
【13-C-4】 「もう業務はとまらない!オフライン機能を使った業務アプリケーションの実例と最新 Curl 情報」
【13-C-4】 「もう業務はとまらない!オフライン機能を使った業務アプリケーションの実例と最新 Curl 情報」【13-C-4】 「もう業務はとまらない!オフライン機能を使った業務アプリケーションの実例と最新 Curl 情報」
【13-C-4】 「もう業務はとまらない!オフライン機能を使った業務アプリケーションの実例と最新 Curl 情報」devsumi2009
 
QM-076-六標準差管理方法的解題邏輯與策略
QM-076-六標準差管理方法的解題邏輯與策略QM-076-六標準差管理方法的解題邏輯與策略
QM-076-六標準差管理方法的解題邏輯與策略handbook
 
網路、設計、使用者經驗
網路、設計、使用者經驗網路、設計、使用者經驗
網路、設計、使用者經驗Charles (XXC) Chen
 

What's hot (17)

Laxham Viajaya Laxham
Laxham Viajaya LaxhamLaxham Viajaya Laxham
Laxham Viajaya Laxham
 
PMT-006-生產計劃與管理
PMT-006-生產計劃與管理PMT-006-生產計劃與管理
PMT-006-生產計劃與管理
 
俄罗斯进出口标准,技术规格,法律,法规,中英文,目录编号RG 2660
俄罗斯进出口标准,技术规格,法律,法规,中英文,目录编号RG 2660俄罗斯进出口标准,技术规格,法律,法规,中英文,目录编号RG 2660
俄罗斯进出口标准,技术规格,法律,法规,中英文,目录编号RG 2660
 
俄罗斯进出口标准,技术规格,法律,法规,中英文,目录编号RG 2681
俄罗斯进出口标准,技术规格,法律,法规,中英文,目录编号RG 2681俄罗斯进出口标准,技术规格,法律,法规,中英文,目录编号RG 2681
俄罗斯进出口标准,技术规格,法律,法规,中英文,目录编号RG 2681
 
俄罗斯Gost标准,进出口购买商品目录№RG 3783
俄罗斯Gost标准,进出口购买商品目录№RG 3783俄罗斯Gost标准,进出口购买商品目录№RG 3783
俄罗斯Gost标准,进出口购买商品目录№RG 3783
 
俄罗斯Gost标准,进出口购买商品目录№RG 425
俄罗斯Gost标准,进出口购买商品目录№RG 425俄罗斯Gost标准,进出口购买商品目录№RG 425
俄罗斯Gost标准,进出口购买商品目录№RG 425
 
Telugu bible 80)_old_testament
Telugu bible 80)_old_testamentTelugu bible 80)_old_testament
Telugu bible 80)_old_testament
 
俄罗斯进出口标准,技术规格,法律,法规,中英文,目录编号RG 2676
俄罗斯进出口标准,技术规格,法律,法规,中英文,目录编号RG 2676俄罗斯进出口标准,技术规格,法律,法规,中英文,目录编号RG 2676
俄罗斯进出口标准,技术规格,法律,法规,中英文,目录编号RG 2676
 
俄罗斯Gost标准,进出口购买商品目录№RG 3757
俄罗斯Gost标准,进出口购买商品目录№RG 3757俄罗斯Gost标准,进出口购买商品目录№RG 3757
俄罗斯Gost标准,进出口购买商品目录№RG 3757
 
multimedia networking
multimedia networkingmultimedia networking
multimedia networking
 
俄罗斯Gost标准,进出口购买商品目录№RG 1306
俄罗斯Gost标准,进出口购买商品目录№RG 1306俄罗斯Gost标准,进出口购买商品目录№RG 1306
俄罗斯Gost标准,进出口购买商品目录№RG 1306
 
Обеспечение безопасности web приложений
Обеспечение безопасности web приложенийОбеспечение безопасности web приложений
Обеспечение безопасности web приложений
 
Test
TestTest
Test
 
Reloaded
ReloadedReloaded
Reloaded
 
【13-C-4】 「もう業務はとまらない!オフライン機能を使った業務アプリケーションの実例と最新 Curl 情報」
【13-C-4】 「もう業務はとまらない!オフライン機能を使った業務アプリケーションの実例と最新 Curl 情報」【13-C-4】 「もう業務はとまらない!オフライン機能を使った業務アプリケーションの実例と最新 Curl 情報」
【13-C-4】 「もう業務はとまらない!オフライン機能を使った業務アプリケーションの実例と最新 Curl 情報」
 
QM-076-六標準差管理方法的解題邏輯與策略
QM-076-六標準差管理方法的解題邏輯與策略QM-076-六標準差管理方法的解題邏輯與策略
QM-076-六標準差管理方法的解題邏輯與策略
 
網路、設計、使用者經驗
網路、設計、使用者經驗網路、設計、使用者經驗
網路、設計、使用者經驗
 

Viewers also liked

Graficas ..[1] De Segundo[1]
Graficas ..[1]  De Segundo[1]Graficas ..[1]  De Segundo[1]
Graficas ..[1] De Segundo[1]mari v.g
 
Zoraide Vani Gnoatto
Zoraide Vani GnoattoZoraide Vani Gnoatto
Zoraide Vani Gnoattozoraideg
 
Primeros Lugar De 1er Bimestre
Primeros Lugar De 1er BimestrePrimeros Lugar De 1er Bimestre
Primeros Lugar De 1er Bimestreest80rafaelramirez
 
Capitulo 3
Capitulo 3Capitulo 3
Capitulo 3Kevin
 
Eyeborg
EyeborgEyeborg
Eyeborgmewtwo
 
Catalogue Cement tiles - Carreaux Ciment
Catalogue Cement tiles - Carreaux CimentCatalogue Cement tiles - Carreaux Ciment
Catalogue Cement tiles - Carreaux Cimentetiennelaude
 
Comparetive Jacquekine
Comparetive JacquekineComparetive Jacquekine
Comparetive Jacquekineieplab
 
About Telecommunication Systems
About Telecommunication SystemsAbout Telecommunication Systems
About Telecommunication SystemsS N M P Simamora
 
Workshop Copywriting
Workshop CopywritingWorkshop Copywriting
Workshop Copywritingdongm
 
0337 1978 Norma Conceptos
0337 1978 Norma Conceptos0337 1978 Norma Conceptos
0337 1978 Norma Conceptosnono pi
 
Zoraide Vani Gnoatto
Zoraide Vani GnoattoZoraide Vani Gnoatto
Zoraide Vani Gnoattozoraideg
 
O Cerrado; conceito e vegetação
O Cerrado; conceito e vegetaçãoO Cerrado; conceito e vegetação
O Cerrado; conceito e vegetaçãoUESPI - PI
 
Josef Hoffmann+
Josef Hoffmann+Josef Hoffmann+
Josef Hoffmann+geexx
 

Viewers also liked (20)

Villa Blandino B&B
Villa Blandino B&BVilla Blandino B&B
Villa Blandino B&B
 
Graficas ..[1] De Segundo[1]
Graficas ..[1]  De Segundo[1]Graficas ..[1]  De Segundo[1]
Graficas ..[1] De Segundo[1]
 
Fegato Ematobilia
Fegato   EmatobiliaFegato   Ematobilia
Fegato Ematobilia
 
Es Nadal
Es NadalEs Nadal
Es Nadal
 
Zoraide Vani Gnoatto
Zoraide Vani GnoattoZoraide Vani Gnoatto
Zoraide Vani Gnoatto
 
Week Van De Democratie
Week Van De DemocratieWeek Van De Democratie
Week Van De Democratie
 
Primeros Lugar De 1er Bimestre
Primeros Lugar De 1er BimestrePrimeros Lugar De 1er Bimestre
Primeros Lugar De 1er Bimestre
 
Capitulo 3
Capitulo 3Capitulo 3
Capitulo 3
 
Eyeborg
EyeborgEyeborg
Eyeborg
 
Blaxos & Louloudis
Blaxos & LouloudisBlaxos & Louloudis
Blaxos & Louloudis
 
Envejecimiento
EnvejecimientoEnvejecimiento
Envejecimiento
 
Catalogue Cement tiles - Carreaux Ciment
Catalogue Cement tiles - Carreaux CimentCatalogue Cement tiles - Carreaux Ciment
Catalogue Cement tiles - Carreaux Ciment
 
Comparetive Jacquekine
Comparetive JacquekineComparetive Jacquekine
Comparetive Jacquekine
 
About Telecommunication Systems
About Telecommunication SystemsAbout Telecommunication Systems
About Telecommunication Systems
 
Topografia sena
Topografia senaTopografia sena
Topografia sena
 
Workshop Copywriting
Workshop CopywritingWorkshop Copywriting
Workshop Copywriting
 
0337 1978 Norma Conceptos
0337 1978 Norma Conceptos0337 1978 Norma Conceptos
0337 1978 Norma Conceptos
 
Zoraide Vani Gnoatto
Zoraide Vani GnoattoZoraide Vani Gnoatto
Zoraide Vani Gnoatto
 
O Cerrado; conceito e vegetação
O Cerrado; conceito e vegetaçãoO Cerrado; conceito e vegetação
O Cerrado; conceito e vegetação
 
Josef Hoffmann+
Josef Hoffmann+Josef Hoffmann+
Josef Hoffmann+
 

Similar to 数学物理漫谈

Telugu bible old testament
Telugu bible old testamentTelugu bible old testament
Telugu bible old testamentWorldBibles
 
Telugu bible old testament
Telugu bible old testamentTelugu bible old testament
Telugu bible old testamentWorldBibles
 
Misc Commands
Misc CommandsMisc Commands
Misc CommandsMija Nam
 
Telugu old testament
Telugu old testamentTelugu old testament
Telugu old testamentHolyBibles
 
保養品大全
保養品大全保養品大全
保養品大全honan4108
 
TELUGU BIBLE.pdf -తెలుగు బైబిల్.pdf
TELUGU BIBLE.pdf -తెలుగు బైబిల్.pdfTELUGU BIBLE.pdf -తెలుగు బైబిల్.pdf
TELUGU BIBLE.pdf -తెలుగు బైబిల్.pdfbiblemissionkarimnagar
 
METRO – Atenas – 04.03.2008
METRO – Atenas – 04.03.2008METRO – Atenas – 04.03.2008
METRO – Atenas – 04.03.2008MANCHETE
 
The Pooooor Ant!
The Pooooor Ant!The Pooooor Ant!
The Pooooor Ant!junk mail
 
「由無痕山林走向上帝」 柏毅
「由無痕山林走向上帝」   柏毅「由無痕山林走向上帝」   柏毅
「由無痕山林走向上帝」 柏毅guest3fcba2b
 
Awadhi new testament
Awadhi new testamentAwadhi new testament
Awadhi new testamentHolyBibles
 
俄罗斯Gost标准,进出口购买商品目录№RG 375
俄罗斯Gost标准,进出口购买商品目录№RG 375俄罗斯Gost标准,进出口购买商品目录№RG 375
俄罗斯Gost标准,进出口购买商品目录№RG 375Turkmenistan Laws
 
俄罗斯Gost标准,进出口购买商品目录№RG 427
俄罗斯Gost标准,进出口购买商品目录№RG 427俄罗斯Gost标准,进出口购买商品目录№RG 427
俄罗斯Gost标准,进出口购买商品目录№RG 427Turkmenistan Laws
 
تغلب على التأجيل
تغلب على التأجيلتغلب على التأجيل
تغلب على التأجيلDr Ghaiath Hussein
 

Similar to 数学物理漫谈 (20)

Telugu bible old testament
Telugu bible old testamentTelugu bible old testament
Telugu bible old testament
 
Telugu bible old testament
Telugu bible old testamentTelugu bible old testament
Telugu bible old testament
 
D1
D1D1
D1
 
1
11
1
 
Misc Commands
Misc CommandsMisc Commands
Misc Commands
 
Telugu old testament
Telugu old testamentTelugu old testament
Telugu old testament
 
保養品大全
保養品大全保養品大全
保養品大全
 
Antaryami
AntaryamiAntaryami
Antaryami
 
TELUGU BIBLE.pdf -తెలుగు బైబిల్.pdf
TELUGU BIBLE.pdf -తెలుగు బైబిల్.pdfTELUGU BIBLE.pdf -తెలుగు బైబిల్.pdf
TELUGU BIBLE.pdf -తెలుగు బైబిల్.pdf
 
METRO – Atenas – 04.03.2008
METRO – Atenas – 04.03.2008METRO – Atenas – 04.03.2008
METRO – Atenas – 04.03.2008
 
Poor Ant
Poor AntPoor Ant
Poor Ant
 
The Pooooor Ant!
The Pooooor Ant!The Pooooor Ant!
The Pooooor Ant!
 
Poor Ant
Poor AntPoor Ant
Poor Ant
 
Poor Ant
Poor AntPoor Ant
Poor Ant
 
「由無痕山林走向上帝」 柏毅
「由無痕山林走向上帝」   柏毅「由無痕山林走向上帝」   柏毅
「由無痕山林走向上帝」 柏毅
 
Awadhi new testament
Awadhi new testamentAwadhi new testament
Awadhi new testament
 
Syn.Egrafa
Syn.EgrafaSyn.Egrafa
Syn.Egrafa
 
俄罗斯Gost标准,进出口购买商品目录№RG 375
俄罗斯Gost标准,进出口购买商品目录№RG 375俄罗斯Gost标准,进出口购买商品目录№RG 375
俄罗斯Gost标准,进出口购买商品目录№RG 375
 
俄罗斯Gost标准,进出口购买商品目录№RG 427
俄罗斯Gost标准,进出口购买商品目录№RG 427俄罗斯Gost标准,进出口购买商品目录№RG 427
俄罗斯Gost标准,进出口购买商品目录№RG 427
 
تغلب على التأجيل
تغلب على التأجيلتغلب على التأجيل
تغلب على التأجيل
 

More from Xu jiakon

33 《学会提问-掌握批判性思维》
33 《学会提问-掌握批判性思维》33 《学会提问-掌握批判性思维》
33 《学会提问-掌握批判性思维》Xu jiakon
 
高中数学知识
高中数学知识高中数学知识
高中数学知识Xu jiakon
 
李克正:精英教育的迫切性与中国教育危机
李克正:精英教育的迫切性与中国教育危机李克正:精英教育的迫切性与中国教育危机
李克正:精英教育的迫切性与中国教育危机Xu jiakon
 
我的数学之路(丘成桐)
我的数学之路(丘成桐)我的数学之路(丘成桐)
我的数学之路(丘成桐)Xu jiakon
 
Internet 信息检索中的数学
Internet 信息检索中的数学Internet 信息检索中的数学
Internet 信息检索中的数学Xu jiakon
 
动态金融风险度量,稳型中心极限定理和G-Brown运动
动态金融风险度量,稳型中心极限定理和G-Brown运动动态金融风险度量,稳型中心极限定理和G-Brown运动
动态金融风险度量,稳型中心极限定理和G-Brown运动Xu jiakon
 
数学竞赛与初等数学研究在中国
数学竞赛与初等数学研究在中国数学竞赛与初等数学研究在中国
数学竞赛与初等数学研究在中国Xu jiakon
 
Professional Development Of Chinese Mathematics Teachers Research A Review Of...
Professional Development Of Chinese Mathematics Teachers Research A Review Of...Professional Development Of Chinese Mathematics Teachers Research A Review Of...
Professional Development Of Chinese Mathematics Teachers Research A Review Of...Xu jiakon
 
艺术院线纳新宣传
艺术院线纳新宣传艺术院线纳新宣传
艺术院线纳新宣传Xu jiakon
 
信息采集与编辑培训(090421)
信息采集与编辑培训(090421)信息采集与编辑培训(090421)
信息采集与编辑培训(090421)Xu jiakon
 
On Mathematics Learning Perspective Among Teachers And Students In China
On Mathematics Learning  Perspective Among Teachers And Students In ChinaOn Mathematics Learning  Perspective Among Teachers And Students In China
On Mathematics Learning Perspective Among Teachers And Students In ChinaXu jiakon
 
The Teaching Of Mathematics At Senior High School In France
The Teaching Of Mathematics At Senior High School In FranceThe Teaching Of Mathematics At Senior High School In France
The Teaching Of Mathematics At Senior High School In FranceXu jiakon
 
An Experimental Study On Students Higher Level Mathematics Cognition
An Experimental Study On Students Higher Level Mathematics CognitionAn Experimental Study On Students Higher Level Mathematics Cognition
An Experimental Study On Students Higher Level Mathematics CognitionXu jiakon
 
☆中高考综合报告[英]
☆中高考综合报告[英]☆中高考综合报告[英]
☆中高考综合报告[英]Xu jiakon
 
福建省数学高考改革与高中数学教育的过去与现在 厦门讲稿
福建省数学高考改革与高中数学教育的过去与现在 厦门讲稿福建省数学高考改革与高中数学教育的过去与现在 厦门讲稿
福建省数学高考改革与高中数学教育的过去与现在 厦门讲稿Xu jiakon
 
数学教育文化与数学英才教育
数学教育文化与数学英才教育数学教育文化与数学英才教育
数学教育文化与数学英才教育Xu jiakon
 
2009年中国数学会学术年会与会者通讯录
2009年中国数学会学术年会与会者通讯录2009年中国数学会学术年会与会者通讯录
2009年中国数学会学术年会与会者通讯录Xu jiakon
 
报告摘要
报告摘要报告摘要
报告摘要Xu jiakon
 
吉林大学讲座信息网前卫南校区宣讲课件
吉林大学讲座信息网前卫南校区宣讲课件吉林大学讲座信息网前卫南校区宣讲课件
吉林大学讲座信息网前卫南校区宣讲课件Xu jiakon
 
我的数学之路(丘成桐)
我的数学之路(丘成桐)我的数学之路(丘成桐)
我的数学之路(丘成桐)Xu jiakon
 

More from Xu jiakon (20)

33 《学会提问-掌握批判性思维》
33 《学会提问-掌握批判性思维》33 《学会提问-掌握批判性思维》
33 《学会提问-掌握批判性思维》
 
高中数学知识
高中数学知识高中数学知识
高中数学知识
 
李克正:精英教育的迫切性与中国教育危机
李克正:精英教育的迫切性与中国教育危机李克正:精英教育的迫切性与中国教育危机
李克正:精英教育的迫切性与中国教育危机
 
我的数学之路(丘成桐)
我的数学之路(丘成桐)我的数学之路(丘成桐)
我的数学之路(丘成桐)
 
Internet 信息检索中的数学
Internet 信息检索中的数学Internet 信息检索中的数学
Internet 信息检索中的数学
 
动态金融风险度量,稳型中心极限定理和G-Brown运动
动态金融风险度量,稳型中心极限定理和G-Brown运动动态金融风险度量,稳型中心极限定理和G-Brown运动
动态金融风险度量,稳型中心极限定理和G-Brown运动
 
数学竞赛与初等数学研究在中国
数学竞赛与初等数学研究在中国数学竞赛与初等数学研究在中国
数学竞赛与初等数学研究在中国
 
Professional Development Of Chinese Mathematics Teachers Research A Review Of...
Professional Development Of Chinese Mathematics Teachers Research A Review Of...Professional Development Of Chinese Mathematics Teachers Research A Review Of...
Professional Development Of Chinese Mathematics Teachers Research A Review Of...
 
艺术院线纳新宣传
艺术院线纳新宣传艺术院线纳新宣传
艺术院线纳新宣传
 
信息采集与编辑培训(090421)
信息采集与编辑培训(090421)信息采集与编辑培训(090421)
信息采集与编辑培训(090421)
 
On Mathematics Learning Perspective Among Teachers And Students In China
On Mathematics Learning  Perspective Among Teachers And Students In ChinaOn Mathematics Learning  Perspective Among Teachers And Students In China
On Mathematics Learning Perspective Among Teachers And Students In China
 
The Teaching Of Mathematics At Senior High School In France
The Teaching Of Mathematics At Senior High School In FranceThe Teaching Of Mathematics At Senior High School In France
The Teaching Of Mathematics At Senior High School In France
 
An Experimental Study On Students Higher Level Mathematics Cognition
An Experimental Study On Students Higher Level Mathematics CognitionAn Experimental Study On Students Higher Level Mathematics Cognition
An Experimental Study On Students Higher Level Mathematics Cognition
 
☆中高考综合报告[英]
☆中高考综合报告[英]☆中高考综合报告[英]
☆中高考综合报告[英]
 
福建省数学高考改革与高中数学教育的过去与现在 厦门讲稿
福建省数学高考改革与高中数学教育的过去与现在 厦门讲稿福建省数学高考改革与高中数学教育的过去与现在 厦门讲稿
福建省数学高考改革与高中数学教育的过去与现在 厦门讲稿
 
数学教育文化与数学英才教育
数学教育文化与数学英才教育数学教育文化与数学英才教育
数学教育文化与数学英才教育
 
2009年中国数学会学术年会与会者通讯录
2009年中国数学会学术年会与会者通讯录2009年中国数学会学术年会与会者通讯录
2009年中国数学会学术年会与会者通讯录
 
报告摘要
报告摘要报告摘要
报告摘要
 
吉林大学讲座信息网前卫南校区宣讲课件
吉林大学讲座信息网前卫南校区宣讲课件吉林大学讲座信息网前卫南校区宣讲课件
吉林大学讲座信息网前卫南校区宣讲课件
 
我的数学之路(丘成桐)
我的数学之路(丘成桐)我的数学之路(丘成桐)
我的数学之路(丘成桐)
 

Recently uploaded

Activity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdfActivity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdfciinovamais
 
Software Engineering Methodologies (overview)
Software Engineering Methodologies (overview)Software Engineering Methodologies (overview)
Software Engineering Methodologies (overview)eniolaolutunde
 
Grant Readiness 101 TechSoup and Remy Consulting
Grant Readiness 101 TechSoup and Remy ConsultingGrant Readiness 101 TechSoup and Remy Consulting
Grant Readiness 101 TechSoup and Remy ConsultingTechSoup
 
Organic Name Reactions for the students and aspirants of Chemistry12th.pptx
Organic Name Reactions  for the students and aspirants of Chemistry12th.pptxOrganic Name Reactions  for the students and aspirants of Chemistry12th.pptx
Organic Name Reactions for the students and aspirants of Chemistry12th.pptxVS Mahajan Coaching Centre
 
Interactive Powerpoint_How to Master effective communication
Interactive Powerpoint_How to Master effective communicationInteractive Powerpoint_How to Master effective communication
Interactive Powerpoint_How to Master effective communicationnomboosow
 
Advanced Views - Calendar View in Odoo 17
Advanced Views - Calendar View in Odoo 17Advanced Views - Calendar View in Odoo 17
Advanced Views - Calendar View in Odoo 17Celine George
 
Q4-W6-Restating Informational Text Grade 3
Q4-W6-Restating Informational Text Grade 3Q4-W6-Restating Informational Text Grade 3
Q4-W6-Restating Informational Text Grade 3JemimahLaneBuaron
 
The Most Excellent Way | 1 Corinthians 13
The Most Excellent Way | 1 Corinthians 13The Most Excellent Way | 1 Corinthians 13
The Most Excellent Way | 1 Corinthians 13Steve Thomason
 
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...EduSkills OECD
 
A Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy ReformA Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy ReformChameera Dedduwage
 
Hybridoma Technology ( Production , Purification , and Application )
Hybridoma Technology  ( Production , Purification , and Application  ) Hybridoma Technology  ( Production , Purification , and Application  )
Hybridoma Technology ( Production , Purification , and Application ) Sakshi Ghasle
 
Arihant handbook biology for class 11 .pdf
Arihant handbook biology for class 11 .pdfArihant handbook biology for class 11 .pdf
Arihant handbook biology for class 11 .pdfchloefrazer622
 
Student login on Anyboli platform.helpin
Student login on Anyboli platform.helpinStudent login on Anyboli platform.helpin
Student login on Anyboli platform.helpinRaunakKeshri1
 
Privatization and Disinvestment - Meaning, Objectives, Advantages and Disadva...
Privatization and Disinvestment - Meaning, Objectives, Advantages and Disadva...Privatization and Disinvestment - Meaning, Objectives, Advantages and Disadva...
Privatization and Disinvestment - Meaning, Objectives, Advantages and Disadva...RKavithamani
 
microwave assisted reaction. General introduction
microwave assisted reaction. General introductionmicrowave assisted reaction. General introduction
microwave assisted reaction. General introductionMaksud Ahmed
 
Introduction to AI in Higher Education_draft.pptx
Introduction to AI in Higher Education_draft.pptxIntroduction to AI in Higher Education_draft.pptx
Introduction to AI in Higher Education_draft.pptxpboyjonauth
 
Accessible design: Minimum effort, maximum impact
Accessible design: Minimum effort, maximum impactAccessible design: Minimum effort, maximum impact
Accessible design: Minimum effort, maximum impactdawncurless
 
How to Make a Pirate ship Primary Education.pptx
How to Make a Pirate ship Primary Education.pptxHow to Make a Pirate ship Primary Education.pptx
How to Make a Pirate ship Primary Education.pptxmanuelaromero2013
 

Recently uploaded (20)

Activity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdfActivity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdf
 
Software Engineering Methodologies (overview)
Software Engineering Methodologies (overview)Software Engineering Methodologies (overview)
Software Engineering Methodologies (overview)
 
Grant Readiness 101 TechSoup and Remy Consulting
Grant Readiness 101 TechSoup and Remy ConsultingGrant Readiness 101 TechSoup and Remy Consulting
Grant Readiness 101 TechSoup and Remy Consulting
 
Organic Name Reactions for the students and aspirants of Chemistry12th.pptx
Organic Name Reactions  for the students and aspirants of Chemistry12th.pptxOrganic Name Reactions  for the students and aspirants of Chemistry12th.pptx
Organic Name Reactions for the students and aspirants of Chemistry12th.pptx
 
Interactive Powerpoint_How to Master effective communication
Interactive Powerpoint_How to Master effective communicationInteractive Powerpoint_How to Master effective communication
Interactive Powerpoint_How to Master effective communication
 
Advanced Views - Calendar View in Odoo 17
Advanced Views - Calendar View in Odoo 17Advanced Views - Calendar View in Odoo 17
Advanced Views - Calendar View in Odoo 17
 
Q4-W6-Restating Informational Text Grade 3
Q4-W6-Restating Informational Text Grade 3Q4-W6-Restating Informational Text Grade 3
Q4-W6-Restating Informational Text Grade 3
 
The Most Excellent Way | 1 Corinthians 13
The Most Excellent Way | 1 Corinthians 13The Most Excellent Way | 1 Corinthians 13
The Most Excellent Way | 1 Corinthians 13
 
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
 
A Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy ReformA Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy Reform
 
Hybridoma Technology ( Production , Purification , and Application )
Hybridoma Technology  ( Production , Purification , and Application  ) Hybridoma Technology  ( Production , Purification , and Application  )
Hybridoma Technology ( Production , Purification , and Application )
 
Arihant handbook biology for class 11 .pdf
Arihant handbook biology for class 11 .pdfArihant handbook biology for class 11 .pdf
Arihant handbook biology for class 11 .pdf
 
TataKelola dan KamSiber Kecerdasan Buatan v022.pdf
TataKelola dan KamSiber Kecerdasan Buatan v022.pdfTataKelola dan KamSiber Kecerdasan Buatan v022.pdf
TataKelola dan KamSiber Kecerdasan Buatan v022.pdf
 
Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"
Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"
Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"
 
Student login on Anyboli platform.helpin
Student login on Anyboli platform.helpinStudent login on Anyboli platform.helpin
Student login on Anyboli platform.helpin
 
Privatization and Disinvestment - Meaning, Objectives, Advantages and Disadva...
Privatization and Disinvestment - Meaning, Objectives, Advantages and Disadva...Privatization and Disinvestment - Meaning, Objectives, Advantages and Disadva...
Privatization and Disinvestment - Meaning, Objectives, Advantages and Disadva...
 
microwave assisted reaction. General introduction
microwave assisted reaction. General introductionmicrowave assisted reaction. General introduction
microwave assisted reaction. General introduction
 
Introduction to AI in Higher Education_draft.pptx
Introduction to AI in Higher Education_draft.pptxIntroduction to AI in Higher Education_draft.pptx
Introduction to AI in Higher Education_draft.pptx
 
Accessible design: Minimum effort, maximum impact
Accessible design: Minimum effort, maximum impactAccessible design: Minimum effort, maximum impact
Accessible design: Minimum effort, maximum impact
 
How to Make a Pirate ship Primary Education.pptx
How to Make a Pirate ship Primary Education.pptxHow to Make a Pirate ship Primary Education.pptx
How to Make a Pirate ship Primary Education.pptx
 

数学物理漫谈

  • 1. SNJ‡ êÆÔnû! ±j ˜uŒÆêƉÆX9úôŒÆêƉƥ% ÜÜêÆØ ÜS, 2005c10' ±j êÆÔnû!
  • 2. SNJ‡ SNJ‡ 1 VØ 2 êÆ[†êÆÔn 3 ²YÔn†êÆ 4 g“Ôn†êÆ 5 y“Ôn†êÆ ±j êÆÔnû!
  • 3. SNJ‡ SNJ‡ 1 VØ 2 êÆ[†êÆÔn 3 ²YÔn†êÆ 4 g“Ôn†êÆ 5 y“Ôn†êÆ ±j êÆÔnû!
  • 4. SNJ‡ SNJ‡ 1 VØ 2 êÆ[†êÆÔn 3 ²YÔn†êÆ 4 g“Ôn†êÆ 5 y“Ôn†êÆ ±j êÆÔnû!
  • 5. SNJ‡ SNJ‡ 1 VØ 2 êÆ[†êÆÔn 3 ²YÔn†êÆ 4 g“Ôn†êÆ 5 y“Ôn†êÆ ±j êÆÔnû!
  • 6. SNJ‡ SNJ‡ 1 VØ 2 êÆ[†êÆÔn 3 ²YÔn†êÆ 4 g“Ôn†êÆ 5 y“Ôn†êÆ ±j êÆÔnû!
  • 7. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ êÆÔn†nØÔn ôv¬§ §^=ŠJ¯µ/UÄwŠ·êÆÔn†nØÔ n'«yº0 2004?a¬ïÄ)±¡xsk^=Š£‰µ/ö'8' ؘ$quot;0ÚzXÖ¿µ/êÆÔn6êƧ nØ Ôn95Ônquot;0 Ágµ/œ'9~ Ѓ'Ï4(2005-9-28) ))Pôv¬Ó“ À©HmêÆïĤ0 ±j êÆÔnû!
  • 8. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ êÆÔn†nØÔn êÆ êÆÔn ÔnÆ nØÔn g,F ±j êÆÔnû!
  • 9. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ Ÿo¬kêÆÔnº ­þ)ÃêÆÔn§‰'õ §Òk ù€Æ¯quot; êÆÚÔn)5Ñ5uég,F'@£quot; Œ´§‚g'uÐq22‡Ñé¢Sy–Ú¯K'ïÄ, UìnØSQ'quot;{¦ugduÐquot; ù«aF'uÐÚ‡Ñv¡w5Øv´êÆ[½ÔnÆ[g „gW'œåiZ§¢¢Sþ22k¿ŽØ '¢SA^quot; ±j êÆÔnû!
  • 10. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ Ÿo¬kêÆÔnº 9XOê´ég,'¯œ§¢êÆ[9©uAûXe'¯ Kµ x n + y n = zn Qn 2žvkš²…'êA(¤çŒ½n¤quot; ù‡¯K'@Ø)vk?Û¢S¿Âquot; êÆ[ Aûù‡¯KuÐ Œ'“êêØ'nØquot; ùnØ'˜Ü©QyQ'OŽÅž“Q—è†cènØ¥ åX­‡Š^quot; ±j êÆÔnû!
  • 11. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ Ÿo¬kêÆÔnº q9XlèGÿþ1¢S¯KuÐѲ¡AÛÆ£ F1¤ Ú‡©AÛ£Gauss)quot; 9u²¡AÛÆ¥k9²I‚'IÊú£v†‚©˜Xk …ak˜^²I‚¤'?Ø— ¤¢'šîAÛquot; ùq¢´˜‡vky¢F'Ä–?ا¢¥¡AÛÚV­ AÛQy“¤”Eâ£XCAT×£¤þkA^quot;  ¡¬! AÛÆQÔn¥'˜A^quot; ±j êÆÔnû!
  • 12. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ Ÿo¬kêÆÔnº ÔnÆ'ïÄ¥k‡quot;äNy–Ú¯K'nØJÑquot; ¢¨B© o«Ä)'Š^åµÚå§b^å§fŠ^å§ rŠ^åquot; ÔnÆ[XEinstein£OÏdquot;¤J¦ùo«Š^å'˜‡ Ú˜'nØquot; d¦‚‰Xˆ«}Á§Jш«nØFquot; ±j êÆÔnû!
  • 13. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ Ÿo¬kêÆÔnº µ§˜‡ÔnF´Ä¤õ'̇sO´´ÄJø ¢¨Œ ±¨y'ýóquot; ùFk'‰Ñ ýó§¢8c'¢¨^‡„Ã{¨y§ ùÜ©'ÔnxŒ±¡ŠnØÔn¶ k'„?QêÆí'0㧄vk‰Ñ¢¨Œ±¨y'ý ó§ùÜ©'ÔnxŒ±¡ŠêÆÔnquot; ±j êÆÔnû!
  • 14. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ êÆ[†êÆÔn êÆÔn'ÑyØ´éÈ'¯œquot; Q²YÔnuÐ'žÏ§Ø ¢¨ÔnÆ[§ÔnÆ[Ó ž´êÆ[§XNewton, Lagrange, Laplace, Fourier, Gauss, Maxwell1quot; Einsteink©ÙuvQêÆD““Mathematische Annalen”þquot; êƆÔnˆg'uЦ§‚Åì©lquot; êÆÔn´êÆ[†ÔnÆ[ŒU¡Ó97'˜+§g c5Åì¹#å5quot; ±j êÆÔnû!
  • 15. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ êÆ[†êÆÔn † g“§˜•Œ'êÆ[é97ÔnÆquot;XHilbert! v5êÆÔn{6§ïÄvPƒéضWeylïÄvP ƒéا!v5žm!˜m!ÔŸ6¶CartanïÄvP ƒéضvon NeumannïÄvþfåÆquot; kêÆ[ϏêÆÔnéêÆ)kXíÄ ïÄêÆ Ôn§¦‚¿vkéÐ'ÔnÔö§é¤ïÄ'é–'Ôn ¿ÂÚÔn폿Ø97quot; ±j êÆÔnû!
  • 16. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ êÆ[†êÆÔn êÆ[Œ±¥b'˜‡¯¢´µ¦‚Œ±UìêÆSQ'S ÆuÐêƧ ØU97¦‚nØ'A^quot; lÔnÆ[@p'‡quot;´µØ´ÔnA^ uÐ'êÆn ØQÔn¥k^quot; ·‡'²¨´µÉÔnÆ[éu¦‚'óŠJøî‚Ä :'êÆóŠ,QêÆþé­‡§¢Ø‡Ï4 ÔnÆ ['3üÚ­Àquot; ±j êÆÔnû!
  • 17. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ uêÆ[†êÆÔn Žk)40c“–¯Princetonp1ïĤ'ž ÿ§EinsteinQgCú¿•¦HÚ˜|Ø'Ž{§F 4¦ëù˜¡'ïÄquot; EinsteinQk)'8‡p˜cgC'©Ù§Œ´ü‡r~ v @©Ù„2Q@quot; Einstein'“Ö5JPk)µ/xoŒ±òEinstein'© Ù˜Q8‡p˜ƒØnQº0 k)Ø@Einstein'Ž{k#n§vk‹‘¦‰Ú˜| ؐ¡'ïħ ´U‰gC'êÆïÄquot; ±j êÆÔnû!
  • 18. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ uêÆ[†êÆÔn A›cv §k)¤uÐ'Chern-WeilnØ ÚChern-SimonsnØQÔn¥P'A^quot; EinsteinQÚ˜|ؐ¡'ãåÄ)þ@´”} § ,¦J¦Ú˜nØ'gŽ˜†ò‰ e5§¤y“nØ ÔnÚêÆÔn'SgŽquot; k•Œ¤Ò'˜½´kÌ„'œ ±j êÆÔnû!
  • 19. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ uêÆ[†êÆÔn uÛŽk)é­ÀêÆÔn'ïħ¦ïÆxÜm¦k) ¥s‰ÆêÆïĤ?˜?ïħonØÔnïÄ¿Ì ?quot; Üm¦k)uêxŒÆêÆX§É’uͶÚOÔnÆ[4 V£R©H©Fowler¤§QÅ£N©Bohr¤Ú |£W. Pauli¤bóŠquot; ¦## u¯k)!£)k)!ûˉk)!Á­k) 1ïÄ)quot; ±j êÆÔnû!
  • 20. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ uêÆ[†êÆÔn ºék)éêÆÔnkÏ'ïħ~Xéuy¨wk )JÑ'S‰|؆‡©AÛéänØ'9X‰Ñv­‡  zquot; ¦## êÆÔnïĐ¡'˜¥jåþquot;y² *¿ ™5ICߎ'±•‰k)Úy²vxõߎ'4Ž¸k) с´¦'ïÄ)quot; ±j êÆÔnû!
  • 21. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ uêÆ[†êÆÔn #‡Ík)Qþ­V²«c“=m©†¨wk)ÜŠcI S‰|ؐ¡'ïħ´·sêÆÔnïÄ'mÿöƒ˜quot; sS„kxõÙ¦l¯êÆÔnïÄ'cêÆ[§QdØ U˜˜J9 quot; ±j êÆÔnû!
  • 22. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ uêÆ[†êÆÔn £¤Ðk)¼Fieldsø'ü‘óŠÑ†êÆÔnk9quot; ¦†SchoenAû' Ÿþߎ´PƒéØ¥'¯Kquot; ¦¤y²'CalabiߎQ‡unØ¥å9…Š^quot; ±j êÆÔnû!
  • 23. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ uêÆ[†êÆÔn £k)4åJ†ÚíÄêÆÔnAy´‡unØ'êÆï Äquot; Q{suêÆFk±¦'Æ)ÌN'˜I“cêÆ[ï ÄêÆÔnquot; QsS§“cÆ)éù˜+„quot;))quot;GdŬ§·Ž ‰˜’Dquot; ±j êÆÔnû!
  • 24. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ ²;Ôn†êÆ ²YÔn¹åÆ!9åÆÚÚOåÆ!b^Æ!IÆ1 ¡quot; §‚^ DÚêÆ'ØÓ©|§éù©|'MáÚuÐå íÄŠ^quot; e¡‰˜{ãquot; ±j êÆÔnû!
  • 25. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ Úî(Newton)åƆ~‡©§| ÚîI½ÆF = maŒ!Šµ d2 m r = F. dt 2 ù´˜‡0~‡©§|§%dЩ ˜ÚЩ„ÝŒ AÑŸX?¿ž' ˜Ú„Ýquot; ±j êÆÔnû!
  • 26. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ kÚå Úî'%kÚå½ÆŒ!Šµ d2 Mm GMm m r = −G 3 r = ( ). dt 2 |r | |r | ´UþÚÄþ 1 ˙ 2 GMm E= mr − 2 |r | ˙ L = r × mr . Åðquot;ddŒíÑmÊV(Kepler)n½Æquot; ±j êÆÔnû!
  • 27. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ .‚KFåƆC©{ ½Â.‚KF(Lagrange)þ ˙ 1 ˙ GMm L(r (t), r (t)) = mr 2 + 2 |r | 阴»r : [t , t ] → R , ½Â.‚KFÈ©µ 0 1 3 t1 ˙ L(r (t), r (t))dt t0 ±j êÆÔnû!
  • 28. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ .‚KFåƆC©{ é.‚KFÈ©'g©ÑEuler-Lagrange§µ d ∂L ∂L − = 0. ˙ dt ∂ xi ∂xi ù1duÚî'%kÚ吧quot; g©{P¦^u‡©AÛ¥µXÿG‚!xÚN ì!MorsenØ1quot; ±j êÆÔnû!
  • 29. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ M—îåƆquot;AÛ l.‚KFþŒ±½Âw—î(Hamilton)þµ H := pi qi − L, i ∂L where qi = xi , pi = ∂qi , i = 1, 2, 3. åÆþvˆ¼êf (p, q)§§'6ЧŒ±!µ d f (p, q) = {H, f (p, q)}. dt ±j êÆÔnû!
  • 30. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ M—îåƆquot;AÛ d?{·, ·}Xe½Â'Ñt(Poisson))Òµ ∂f ∂g ∂f ∂g {f , g} = ( − ). ∂qi ∂pi ∂pi ∂qi i w—îåÆ-u ‡©AÛÆ¥4AÛÚÑtAÛ'u Ðquot; Ï~iùAÛ¥§iùÝþ˜­0é¡Üþ§ 4@¨½ Ñt@¨­0‡¡Üþquot; ±j êÆÔnû!
  • 31. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ 9åÆÚÚOåÆ ·é„vkÆvõ£‡È©'žÿÆ9åÆ'aúPÁc 5quot;ƒ8éõkaq'²{quot; ÚOåÆ|^VÇÚO'gŽd‡B6Äí÷By–§ù rc VÇØÚÚOÆ'uÐquot; ÚOåƏþfåÆ'uЋe gŽþ'Ä:quot; ±j êÆÔnû!
  • 32. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ ^Ɔõ£‡È© b^Æ´õ£‡È©A^'IŸ‰~quot; ŒêÆ[Gaussë†v§'uЧQb^Æk˜‡Ônþ 'ü ±¦·¶quot; b^Æ'uÐv§¥¢¨åX9…Š^§¢´ò§í IŸ 'ºX'%´êÆ'Äquot; ðŽd‰(Maxwell)±¦'êÆõåò˜¢¨y–o@ ˜êƐ§quot; ±j êÆÔnû!
  • 33. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ ðŽd‰§ ðŽd‰ÄuêÆþ{'Ä '§Ð†ÔnÆ[ '˜½ÆØΧ 5y²´ÔnÆ[ᆠquot; ðŽd‰l¦'§‰Ñ b^Å'ýóÚIb^Å'ß Ž§ 5Ñ ¢¨y¢quot; e¡o‡§yQ¡ðŽd‰§µ · E = 4πρ, · H = 0, 1 ∂H 1 ∂H 4π ×E + = 0, ×H − = J. c ∂t c ∂t c ±j êÆÔnû!
  • 34. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ ðŽd‰§†^Å Qý˜¥§k 1 ∂H 1 ∂H ×E + = 0, ×H − = 0. c ∂t c ∂t %k 1 ∂E 2 1 ∂H 2 = E, = H. c 2 ∂t c 2 ∂t =E ÚH ÷vÅЧ, dd‰Ñb^Å'ýóquot; ±j êÆÔnû!
  • 35. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ ðŽd‰§†dƒéØ ðŽd‰§'ïÄ',˜‡­‡@t´dƒéØquot; {.I(Faraday)’ ŠI'DÂ'HŸ'±'V gquot; ðŽd‰5¿ Xt±´'½'§QØÓ'ëìXeI„ ØÓquot; ù†ðŽÖ(Michelson)'Ͷ¢¨ØÎquot; ±j êÆÔnû!
  • 36. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ ðŽd‰§†dƒéØ âÔ[(Lorentz)ÚOÏdquot;(Einstein) ´QdÄ:þuÐ dƒéا‰Ñ 5'ž˜Bquot; DŒÅdÄ(Minkowski)‰Ñ'êÆAº^ ‚S“ꥂ Sg†'VgµžmÚ˜m¨¤˜‡o‘˜mµ R4 = {(t, x, y, z) : t, x, y, z ∈ R}, ØÓëìXƒm'‹sd‚Sg† (t , x , y , z ) = (t, x, y, z)A ‰Ñ£A˜o0¤§¦ −c 2 dt 2 +dx 2 +dy 2 +dz 2 = −c 2 (dt )2 +(dx )2 +(dy )2 +(dz )2 . ±j êÆÔnû!
  • 37. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ ðŽd‰§†5‰|Ø ðŽd‰Qí¦'§ž§^ b^³'Vgquot; ÔnÆ[¦5±ù´˜‡êÆóä§vkÔn¿Âquot;  5'uÐy²§b^³´Ä)'Ônþ§Ø Q¢¨ þk¤¢Born-Aharonov¨A§QnØþ†—S‰| Ø'Ñyquot; ±j êÆÔnû!
  • 38. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ C“Ôn†êÆ ·ùp`'g“Ôn'´PƒéØ!þfåÆÚS‰| Øquot; §‚^ þ˜­VkŒuÐ'xõêÆ©|µ‡©AÛ!ÿ ÀÆ!v«Ø1quot; ±j êÆÔnû!
  • 39. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ 2ƒéرc‡©AÛ £pd¤dGGÿþ'¯KÑu§ïÄn‘˜m¥' Gauss ­¡nØquot; Q¦'Ä:þ§Riemann£iù¤JÑ ‡©AÛ'nØÄ :quot; éiùAÛ'ïÄ¥Ñy'Üþ©ÛQåÆïÄ¥kPA ^quot; ùž®Ñy ChristoffelÎÒ1quot; ±j êÆÔnû!
  • 40. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ 2ƒé؆‡©AÛ iùAÛ'•ŒA^´Einstein£OÏdquot;¤Má'Pƒ éØquot; PƒéØÑuX´^‘­LorentzÝþ'6G5£ãž ˜§Einstein§òAÛþ(Ricci­Ç¤†Ônþ£Uþ¨Ä þÜþ¤éXå5quot; êÆ[FËA(Hilbert)^g©{íÑ ý˜¥ 'Einstein§§¢¦gC`vk=‡êÆ[Œ±“ OEinsteinquot; ±j êÆÔnû!
  • 41. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ 2ƒéØ¢¨yâ PƒéØ'k±eýóµY@Y#'cÄ!I‚'­! çÉ'Q!ÚåÅ11quot; Y@Y#'cÄQPƒéØJѱcÒB© quot; PƒéØJÑØȧu) ˜gF quot;˜‡Bÿ¢|Bÿ I‚QNg'­quot; ¨˜‡Æ)¯¦µXtvk y¢§¦¬xo`quot;OÏd quot;£‰µ/@o§·ÐŠO'þPa ¢Ãquot;ÃØX Û§ù‡nØ´ ('quot;0 ±j êÆÔnû!
  • 42. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ 2ƒéØ¢¨yâ çɏkéõBÿyâquot;k'´HawkingÚPenrose^ ‡©ÿÀÆØyçÉ'QSquot; PƒéØ'˜‡­‡íØ´Ä'‰»Fµ‰»´Aä ½Â 'quot;ùdwÇ(Hubble)'Bÿ¤|±quot; †dƒ9'k‰»'Œ¿åFquot;ù‡F'ýóƒ˜ ´‰»¥QµË§ù®Bÿ quot; ÚåÅ'Bÿ´¨V˜‡­‡'‘8quot; ±j êÆÔnû!
  • 43. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ 2ƒé؆y“‡©AÛ PƒéØQêÆþ'­Œ¿Â´4Œ'rc ‡©AÛ' uÐquot; CartanÚWeylс}ÁòEinstein'Úån؆Maxwell' b^nØÚ˜å5§d¦‚¦^ ‡©AÛ¥'éän Øquot; QCartan'󊥧©‡©GªÚÌm1AÛé–uÐå5 §ù‡©AÛ†“êÿÀ'@Ü‹e Ä:quot; ±j êÆÔnû!
  • 44. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ Žk)†y“‡©AÛ Žk)¤uÐ'a'nØ´˜‡Øe'IŸºXquot; k)u CartanQ‡©AÛ¥¦^©‡©Gª'DÚquot; ¦uÐ'^‡©Gª“v«Sa!^‡©Gª'‡Ý ?«Sa(Chern-SimonsnØ!Bott-ChernV­‡Ý¤1Ñ ´4'gŽquot; QÜ•²k)'§w¥k['Hquot; ±j êÆÔnû!
  • 45. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ Žk)†y“‡©AÛ k)'óŠPK ‡©AÛ!“êAÛ!“êêØ! “êÿÀ1õ‡+quot; ¦'óŠµdµ/ÙKr9¤kêÆ+quot;0 Ù¥c­‡'´Atiyah!Singer1uÐ'snØquot;  ¡¬! ¦‚QÔn¥'A^quot; ±j êÆÔnû!
  • 46. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ Einstein †£¤Ðk) †k)ØÓ †Cartanƒaq§£¤Ðk)k)š~97 ÔnÆquot; ¦¼Fieldsø'ü‘óŠÑ†Einsteink9µ˜‘´P ƒéØ¥' Ÿþߎ§˜‘´9uKahler-EinsteinÝþ ¨ 'Calabiߎquot; XtEinsteiné¦!{¬´Ÿo$'|µ§U¢‰·‚ 'Ž–åuž quot; ±j êÆÔnû!
  • 47. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ þfn؆VÇØ þ˜­VÊ›c“±c†PƒéØ|{'´þfåÆquot; †EinsteinA¢˜ïá PƒéØ'nØe¨Ø Ó§þfåÆ´QxõÔnÆ['¡ÓãåeuÐå5'§ Ùv§¥kxõ¹¢ÚØquot; ~X§QþfåÆ¥éÔŸ6Äæ^ aq9åÆ¥'VÇ Aºquot; ,Einstein)éIb¨A'Aº¦¦¤þfnØ'M ©ƒ˜§¦éBrown6ĉv­‡ïħ¦éù«Aº ±~¦Ýquot; ±j êÆÔnû!
  • 48. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ Einstein †þfnØ D`¦éÀ`µ/J#‚ý'ƒ8þP‚•f¯ íº0À£¹#µ/·‚ØUþPTxo‰œ0 Einstein¨céþfåÆ'˜Ÿ¦¤ yQþf8EÆ' ÑuX§Qù‡+gc5k˜¢¨§X¢ï•ë†'˜ ¢¨quot; ùpJ ù´ rx±eêÆÚÔn'ØÓµ¢¨´u ¨ÔnnØ'ªsOquot;·‚¬w vknØ'kI? اk¢¨Ãl‰åquot; ±j êÆÔnû!
  • 49. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ þfåƆ¼©Û bf7X¦fØ”='FkéŒ'(JµdMaxwell'n اbfQ”=v§¥¬uÑb^Ë ›”Uþ§ªá ¦fØþquot; ù«Ë'ȈAT´ë‰'§Œ¢SBÿ'IÌ´lÑ 'quot; þfåÆ¥'˜‡Aºdk¶'Ž™§‰Ñµ ∂ i ψ = Hψ ∂t d?H ˜0‡©Žfquot; ±j êÆÔnû!
  • 50. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ þfåƆ¼©Û ùžŒ±¦^ ‡©§½¼©Û'nصH 'Ì´lÑ '§éAXbf6Ä'U?§U?ƒm'yéAXË' IÌquot; þfåÆrc ¼©Û'uеVon Neumann1ë† þfåƆ¼©Û'ïÄquot; ±j êÆÔnû!
  • 51. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ þfåƆ+Ø þfåÆ¥g”†Äþ'ïÄïá †êÆ¥+ØÚv« ؃m'éXquot; êÆ[Weyl, Van Der WaerdenÑ!v+؆þfåƐ¡ 'Öquot; êÆ[Harish-Chandra¦5´ÆÔn'§dué+ØÚv« ØaD§=¤têÆ'quot; ±j êÆÔnû!
  • 52. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ Dirac § ldƒéØ'ŸþUþ9XŒ±ÑKlein-Gordan§quot; ù´˜‡0¡‡©§quot; duSchrodinger§¥éžm'ê´˜0'§Dirac£A ¨ .Ž¤Ä ¤¢Klein-Gordan§'”²Š”§=k¶ 'Dirac§quot; ù‡§'ý󃘴 bf'Q§du¨ž„vkBÿ bf§DiracY éõ'‹§§9X5gHeisenbergquot; ±j êÆÔnû!
  • 53. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ Dirac §†InØ Dirac'Ž{QêÆþ´Ñ¢¿'§QsnØ¥å9 …Š^quot;AityahÚSingeruÐ'snØ'I˜ÚÒ´‡Q ˜„'6Gþ¨iDiracŽfquot; s½nåuRiemann-RochúªÚGauss-Bonnetúª§ QaÚ'bnØ'Ä:þ§Hirzebruchy² p‘ 'Riemann-RochúªÚÎÒúª£Ç©dk)Qù¡ kóŠ¤quot; Hirzebruch'óŠÚu GrothendieckQù¡'󊧁 ª— AityahÚSingeruÐ'snاÙI˜ÚÒ´‡ Q˜„'6Gþ¨iDiracŽfquot; ±j êÆÔnû!
  • 54. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ Feynman È© l²YåÆ þfåÆkü«YµlHamiltonåÆÑu§ ^ uþfz'{Œ± Schrodinger§¶ ¨ lLagrangeåÆÑu§Œ±—FeynmanÈ©quot; Feynman'{åuDiracÖ¥˜‡¢'remark§ÙÄ) é–´Ä´»˜mþ'È©quot; ùaÈ©êÆþ˜„vkÂ(,kWienerÿÝ'n ؤ§¢ÔnÆ[uÐј{§Œ±‰ÑkÔn¿Â' ýóquot; ±j êÆÔnû!
  • 55. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ Feynman È© È©QÔn¥PA^§ÔnÆ[^§Œ± Feynman êÆþ¿ŽØ '@t§¤±êÆ[@´ÔnÆ[' Û{¥quot; êÆ[¤‰'22´^êƐ{y²ÔnÆ['˜ßŽ§ ØU AÔnÆ[ˆ ùߎ'g´quot; ±j êÆÔnû!
  • 56. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ y“nØÔnÚêÆ ·¤`'y“nØÔn)±Yang-MillsS‰|؏Ä:' þf|Ø!±Pƒé؏Ä:'þfÚånØÚ±Ú˜ù üöª48s'‡unØquot; §‚'¡ÓAX´6^ quot;5quot;õ'y“êƵ‡©AÛ! “êAÛ!ÿÀÆ!v«Ø11quot; §‚¥xõïďquot;5quot;õ'vyêÆÔn§ ØnA nØÔnquot; ±j êÆÔnû!
  • 57. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ y“nØÔnÚêÆ é­‡'´§duêÆÔnªÆ‰'¦^êƧ‚'ïÄr c êÆ)'uÐquot; ~X§éS‰|Ø'ïÄ— Donaldsonn Ø!Seiberg-WittennØ'Ñy§§‚Jø DÚ'‡©ÿ À¤ØUJø'5'{quot; ­‘þfÚå'ïÄ— “êAÛ¥Riemann¡'˜m 'Wittenߎ'ÑyÚKontsevich 'y²quot; ±j êÆÔnû!
  • 58. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ ‡unØ ‡unØq¢êÆ'Ú˜åX錊^quot; §r¤ vertex operator algebra, Gromov-Witten theory and mirror symmetry11'#)quot; du£¤Ðk)y²Calabiߎ Ñy'Calabi-Yau6GQ ‡unØïÄ¥åØ7Š^quot; ‡unØ¥éóS'gŽ— éõ-¯Û'ߎ§k ®²êÆ[y² quot; ±j êÆÔnû!
  • 59. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ dužm9XØU‰['Hquot; Œ±ëoœ'Ö5‡unØüÂ6Ú·'© Ùµ”Derivatives in Mathematics and Physics” quot; Brian Green'Ö5‰»'Œu6£The Elegant Universe). ±j êÆÔnû!
  • 60. êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ (Š ÛÏgS§)g˜À¶ ” ÛÏgS§)Ø)«¶ ÛÏgS§)gäv¶ ÛÏgS§)ÃÄ~¶ ÛÏgS§U)%{quot;” —58yŒ“{¥²6 ±j êÆÔnû!