数学物理漫谈

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数学物理漫谈

  1. 1. SNJ‡ êÆÔnû! ±j ˜uŒÆêƉÆX9úôŒÆêƉƥ% ÜÜêÆØ ÜS, 2005c10' ±j êÆÔnû!
  2. 2. SNJ‡ SNJ‡ 1 VØ 2 êÆ[†êÆÔn 3 ²YÔn†êÆ 4 g“Ôn†êÆ 5 y“Ôn†êÆ ±j êÆÔnû!
  3. 3. SNJ‡ SNJ‡ 1 VØ 2 êÆ[†êÆÔn 3 ²YÔn†êÆ 4 g“Ôn†êÆ 5 y“Ôn†êÆ ±j êÆÔnû!
  4. 4. SNJ‡ SNJ‡ 1 VØ 2 êÆ[†êÆÔn 3 ²YÔn†êÆ 4 g“Ôn†êÆ 5 y“Ôn†êÆ ±j êÆÔnû!
  5. 5. SNJ‡ SNJ‡ 1 VØ 2 êÆ[†êÆÔn 3 ²YÔn†êÆ 4 g“Ôn†êÆ 5 y“Ôn†êÆ ±j êÆÔnû!
  6. 6. SNJ‡ SNJ‡ 1 VØ 2 êÆ[†êÆÔn 3 ²YÔn†êÆ 4 g“Ôn†êÆ 5 y“Ôn†êÆ ±j êÆÔnû!
  7. 7. 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!
  8. 8. VØ êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ êÆÔn†nØÔn êÆ êÆÔn ÔnÆ nØÔn g,F ±j êÆÔnû!
  9. 9. 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'uÐڇÑv¡w5Øv´êÆ[½ÔnÆ[g „gW'œåiZ§¢¢Sþ22k¿ŽØ '¢SA^quot; ±j êÆÔnû!
  10. 10. 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!
  11. 11. VØ êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ Ÿo¬kêÆÔnº q9XlèGÿþ1¢S¯KuÐѲ¡AÛÆ£ F1¤ ڇ©AÛ£Gauss)quot; 9u²¡AÛÆ¥k9²I‚'IÊú£v†‚©˜Xk …ak˜^²I‚¤'?ؗ ¤¢'šîAÛquot; ùq¢´˜‡vky¢F'Ė?ا¢¥¡AÛÚV­ AÛQy“¤”Eâ£XCAT×£¤þkA^quot;  ¡¬! AÛÆQÔn¥'˜A^quot; ±j êÆÔnû!
  12. 12. 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'˜‡ ژ'nØquot; d¦‚‰Xˆ«}Á§Jш«nØFquot; ±j êÆÔnû!
  13. 13. 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!
  14. 14. 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!
  15. 15. 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!ԟ6¶CartanïÄvP ƒéضvon NeumannïÄvþfåÆquot; kêÆ[ϏêÆÔnéêÆ)kXíÄ ïÄêÆ Ôn§¦‚¿vkéÐ'ÔnÔö§é¤ïÄ'é–'Ôn ¿ÂÚÔn폿Ø97quot; ±j êÆÔnû!
  16. 16. 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,QêÆþ魇§¢Ø‡Ï4 ÔnÆ ['3üÚ­Àquot; ±j êÆÔnû!
  17. 17. VØ êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ uêÆ[†êÆÔn Žk)40c“–¯Princetonp1ïĤ'ž ÿ§EinsteinQgCú¿•¦Hژ|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'© ٘Q8‡p˜ƒØnQº0 k)Ø@Einstein'Ž{k#n§vk‹‘¦‰Ú˜| ؐ¡'ïħ ´U‰gC'êÆïÄquot; ±j êÆÔnû!
  18. 18. 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; EinsteinQژ|ؐ¡'ãåÄ)þ@´”} § ,¦J¦Ú˜nØ'gŽ˜†ò‰ e5§¤y“nØ ÔnÚêÆÔn'SgŽquot; k•Œ¤Ò'˜½´k̄'œ ±j êÆÔnû!
  19. 19. VØ êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ uêÆ[†êÆÔn uێk)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. 20. 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!
  21. 21. VØ êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ uêÆ[†êÆÔn #‡Ík)Qþ­V²«c“=m©†¨wk)܊cI S‰|ؐ¡'ïħ´·sêÆÔnïÄ'mÿöƒ˜quot; sS„kxõÙ¦l¯êÆÔnïÄ'cêÆ[§QdØ U˜˜J9 quot; ±j êÆÔnû!
  22. 22. 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!
  23. 23. 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!
  24. 24. 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 íĊ^quot; e¡‰˜{ãquot; ±j êÆÔnû!
  25. 25. 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 AџX?¿ž' ˜Ú„Ýquot; ±j êÆÔnû!
  26. 26. 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!
  27. 27. 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!
  28. 28. 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!
  29. 29. 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!
  30. 30. 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!
  31. 31. 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!
  32. 32. 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!
  33. 33. VØ 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. 34. 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!
  35. 35. 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!
  36. 36. 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†'Vgµžmژm¨¤˜‡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. 37. 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!
  38. 38. 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!
  39. 39. 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!
  40. 40. 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!
  41. 41. 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!
  42. 42. 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!
  43. 43. 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^nØژå5§d¦‚¦^ ‡©AÛ¥'éän Øquot; QCartan'󊥧©‡©GªÚÌm1AÛé–uÐå5 §ù‡©Aۆ“êÿÀ'@܋e Ä:quot; ±j êÆÔnû!
  44. 44. 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; Qܕ²k)'§w¥k['Hquot; ±j êÆÔnû!
  45. 45. 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!
  46. 46. 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˜‘´P ƒéØ¥' Ÿþߎ§˜‘´9uKahler-EinsteinÝþ ¨ 'Calabiߎquot; XtEinsteiné¦!{¬´Ÿo$'|µ§U¢‰·‚ 'Ž–åuž quot; ±j êÆÔnû!
  47. 47. VØ êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ þfn؆VÇØ þ˜­Vʛc“±c†PƒéØ|{'´þfåÆquot; †EinsteinA¢˜ïá PƒéØ'nØe¨Ø Ó§þfåÆ´QxõÔnÆ['¡ÓãåeuÐå5'§ Ùv§¥kxõ¹¢ÚØquot; ~X§QþfåÆ¥éԟ6Äæ^ aq9åÆ¥'VÇ Aºquot; ,Einstein)éIb¨A'Aº¦¦¤þfnØ'M ©ƒ˜§¦éBrown6ĉv­‡ïħ¦éù«Aº ±~¦Ýquot; ±j êÆÔnû!
  48. 48. 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!
  49. 49. VØ êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ þfåƆ¼©Û bf7X¦fؔ='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. 50. 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!
  51. 51. 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!
  52. 52. VØ êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ Dirac § ldƒéØ'ŸþUþ9XŒ±ÑKlein-Gordan§quot; ù´˜‡0¡‡©§quot; duSchrodinger§¥éžm'괘0'§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. 53. 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!
  54. 54. 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) 閴Ä´»˜mþ'È©quot; ùaÈ©êÆþ˜„vkÂ(,kWienerÿÝ'n ؤ§¢ÔnÆ[uÐј{§Œ±‰ÑkÔn¿Â' ýóquot; ±j êÆÔnû!
  55. 55. 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!
  56. 56. VØ êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ y“nØÔnÚêÆ ·¤`'y“nØÔn)±Yang-MillsS‰|؏Ä:' þf|Ø!±Pƒé؏Ä:'þfÚånØڱژù 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. 57. VØ êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ y“nØÔnÚêÆ é­‡'´§duêÆÔnªÆ‰'¦^êƧ‚'ïÄr c êÆ)'uÐquot; ~X§éS‰|Ø'ïė Donaldsonn Ø!Seiberg-WittennØ'Ñy§§‚Jø DÚ'‡©ÿ À¤ØUJø'5'{quot; ­‘þfÚå'ïė “êAÛ¥Riemann¡'˜m 'Wittenߎ'ÑyÚKontsevich 'y²quot; ±j êÆÔnû!
  58. 58. VØ êÆ[†êÆÔn ²;Ôn†êÆ C“Ôn†êÆ y“Ôn†êÆ ‡unØ ‡unØq¢êÆ'ژåX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. 59. 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!
  60. 60. 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!

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