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# 数学物理漫谈

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### 数学物理漫谈

1. 1. SNJ êÆÔnû! ±j uÆêÆÆX9úôÆêÆÆ¥% 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¬§ §^=J¯µ/UÄw·êÆÔnnØÔ n'«yº0 2004?a¬ïÄ)±¡xsk^=£µ/ö'8' Ø\$quot;0ÚzXÖ¿µ/êÆÔn6êÆ§ nØ Ôn95Ônquot;0 Ágµ/'9~ Ð'Ï4(2005-9-28) ))Pôv¬Ó À©HmêÆïÄ¤0 ±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 o¬kêÆÔnº ­þ)ÃêÆÔn§'õ §Òk ùÆ¯quot; êÆÚÔn)5Ñ5uég,F'@£quot; ´§g'uÐq22Ñé¢SyÚ¯K'ïÄ, UìnØSQ'quot;{¦ugduÐquot; ù«aF'uÐÚÑv¡w5Øv´êÆ[½ÔnÆ[g gW'åiZ§¢¢Sþ22k¿Ø '¢SA^quot; ±j êÆÔnû!
10. 10. VØ êÆ[êÆÔn ²;ÔnêÆ CÔnêÆ yÔnêÆ o¬kêÆÔnº 9XOê´ég,'¯§¢êÆ[9©uAûXe'¯ Kµ x n + y n = zn Qn 2vk²'êA(¤ç½n¤quot; ù¯K'@Ø)vk?Û¢S¿Âquot; êÆ[ Aûù¯KuÐ 'êêØ'nØquot; ùnØ'Ü©QyQ'OÅQècènØ¥ åX­^quot; ±j êÆÔnû!
11. 11. VØ êÆ[êÆÔn ²;ÔnêÆ CÔnêÆ yÔnêÆ o¬kêÆÔnº q9XlèGÿþ1¢S¯KuÐÑ²¡AÛÆ£ F1¤ Ú©AÛ£Gauss)quot; 9u²¡AÛÆ¥k9²I'IÊú£v©Xk ak^²I¤'?Ø ¤¢'îAÛquot; ùq¢´vky¢F'Ä?Ø§¢¥¡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 o¬kêÆÔnº ÔnÆ'ïÄ¥kquot;äNyÚ¯K'nØJÑquot; ¢¨B© o«Ä)'^åµÚå§b^å§f^å§ r^åquot; ÔnÆ[XEinstein£OÏdquot;¤J¦ùo«^å' Ú'nØquot; d¦X«}Á§JÑ«nØFquot; ±j êÆÔnû!
13. 13. VØ êÆ[êÆÔn ²;ÔnêÆ CÔnêÆ yÔnêÆ o¬kêÆÔnº µ§ÔnF´Ä¤õ'ÌsO´´ÄJø ¢¨ ±¨y'ýóquot; ùFk'Ñ ýó§¢8c'¢¨^Ã{¨y§ ùÜ©'Ônx±¡nØÔn¶ k'?QêÆí'0ã§vkÑ¢¨±¨y'ý ó§ùÜ©'Ônx±¡êÆÔnquot; ±j êÆÔnû!
14. 14. VØ êÆ[êÆÔn ²;ÔnêÆ CÔnêÆ yÔnêÆ êÆ[êÆÔn êÆÔn'ÑyØ´éÈ'¯quot; Q²YÔnuÐ'Ï§Ø ¢¨ÔnÆ[§ÔnÆ[Ó ´êÆ[§XNewton, Lagrange, Laplace, Fourier, Gauss, Maxwell1quot; Einsteink©ÙuvQêÆD“Mathematische Annalen”þquot; êÆÔng'uÐ¦§Åì©lquot; êÆÔn´êÆ[ÔnÆ[U¡Ó97'+§g c5Åì¹#å5quot; ±j êÆÔnû!
15. 15. VØ êÆ[êÆÔn ²;ÔnêÆ CÔnêÆ yÔnêÆ êÆ[êÆÔn  g§'êÆ[é97ÔnÆquot;XHilbert! v5êÆÔn{6§ïÄvPÂéØ¶WeylïÄvP ÂéØ§!v5m!m!Ô6¶CartanïÄvPÂ éØ¶von NeumannïÄvþfåÆquot; kêÆ[ÏêÆÔnéêÆ)kXíÄ ïÄêÆ Ôn§¦¿vkéÐ'ÔnÔö§é¤ïÄ'é'Ôn ¿ÂÚÔní¿Ø97quot; ±j êÆÔnû!
16. 16. VØ êÆ[êÆÔn ²;ÔnêÆ CÔnêÆ yÔnêÆ êÆ[êÆÔn êÆ[±¥b'¯¢´µ¦±UìêÆSQ'S ÆuÐêÆ§ ØU97¦nØ'A^quot; lÔnÆ[@p'quot;´µØ´ÔnA^ uÐ'êÆn ØQÔn¥k^quot; ·'²¨´µÉÔnÆ[éu¦'óJøîÄ :'êÆó,QêÆþé­§¢ØÏ4 ÔnÆ ['3üÚ­Àquot; ±j êÆÔnû!
17. 17. VØ êÆ[êÆÔn ²;ÔnêÆ CÔnêÆ yÔnêÆ uêÆ[êÆÔn k)40c¯Princetonp1ïÄ¤' ÿ§EinsteinQgCú¿¦HÚ|Ø'{§F 4¦ëù¡'ïÄquot; EinsteinQk)'8pcgC'©Ù§´ür~ v @©Ù2Q@quot; Einstein'Ö5JPk)µ/xo±òEinstein'© ÙQ8pØnQº0 k)Ø@Einstein'{k#n§vk¦Ú| Ø¡'ïÄ§ ´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; EinsteinQÚ|Ø¡'ãåÄ)þ@´} § ,¦J¦ÚnØ'gò e5§¤ynØ ÔnÚêÆÔn'Sgquot; k¤Ò'½´kÌ' ±j êÆÔnû!
19. 19. VØ êÆ[êÆÔn ²;ÔnêÆ CÔnêÆ yÔnêÆ uêÆ[êÆÔn uÛk)é­ÀêÆÔn'ïÄ§¦ïÆxÜm¦k) ¥sÆêÆïÄ¤??ïÄ§onØÔnïÄ¿Ì ?quot; Üm¦k)uêxÆêÆX§ÉuÍ¶ÚOÔnÆ[4 V£R©H©Fowler¤§QÅ£N©Bohr¤Ú |£W. Pauli¤bóquot; ¦## u¯k)!£)k)!ûËk)!Á­k) 1ïÄ)quot; ±j êÆÔnû!
20. 20. VØ êÆ[êÆÔn ²;ÔnêÆ CÔnêÆ yÔnêÆ uêÆ[êÆÔn ºék)éêÆÔnkÏ'ïÄ§~Xéuy¨wk )JÑ'S|Ø©AÛéänØ'9XÑv­  zquot; ¦## êÆÔnïÄ¡'¥jåþquot;y² *¿ 5ICß'±k)Úy²vxõß'4¸k) Ñ´¦'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)ÜcI S|Ø¡'ïÄ§´·sêÆÔnïÄ'mÿö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óÑêÆÔnk9quot; ¦SchoenAû' þß´PÂéØ¥'¯Kquot; ¦¤y²'CalabißQunØ¥å9^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;GdÅ¬§· 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 íÄ^quot; e¡{ãquot; ±j êÆÔnû!
25. 25. VØ êÆ[êÆÔn ²;ÔnêÆ CÔnêÆ yÔnêÆ Úî(Newton)åÆ~©§| ÚîI½ÆF = ma!µ d2 m r = F. dt 2 ù´0~©§|§%dÐ© ÚÐ©Ý AÑX?¿' ÚÝquot; ±j êÆÔnû!
26. 26. VØ êÆ[êÆÔn ²;ÔnêÆ CÔnêÆ yÔnêÆ kÚå Úî'%kÚå½Æ!µ d2 Mm GMm m r = −G 3 r = ( ). dt 2 |r | |r | ´UþÚÄþ 1 ˙ 2 GMm E= mr − 2 |r | ˙ L = r × mr . Åðquot;ddíÑmÊV(Kepler)n½Æquot; ±j êÆÔnû!
27. 27. VØ êÆ[êÆÔn ²;ÔnêÆ CÔnêÆ yÔnêÆ .KFåÆC©{ ½Â.KF(Lagrange)þ ˙ 1 ˙ GMm L(r (t), r (t)) = mr 2 + 2 |r | é´»r : [t , t ] → R , ½Â.KFÈ©µ 0 1 3 t1 ˙ L(r (t), r (t))dt t0 ±j êÆÔnû!
29. 29. VØ êÆ[êÆÔn ²;ÔnêÆ CÔnêÆ yÔnêÆ MîåÆquot;AÛ l.KFþ±½Âwî(Hamilton)þµ H := pi qi − L, i ∂L where qi = xi , pi = ∂qi , i = 1, 2, 3. åÆþv¼êf (p, q)§§'6Ä§±!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îåÆquot;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©'ÿÆ9åÆ'aúPÁc 5quot;8éõkaq'²{quot; ÚOåÆ|^VÇÚO'gdB6Äí÷By§ù rc VÇØÚÚOÆ'uÐquot; ÚOåÆþfåÆ'uÐe gþ'Ä:quot; ±j êÆÔnû!
32. 32. VØ êÆ[êÆÔn ²;ÔnêÆ CÔnêÆ yÔnêÆ ^Æõ£È© b^Æ´õ£È©A^'I~quot; êÆ[Gaussëv§'uÐ§Qb^ÆkÔnþ 'ü ±¦·¶quot; b^Æ'uÐv§¥¢¨åX9^§¢´ò§í I 'ºX'%´êÆ'Äquot; ðd(Maxwell)±¦'êÆõåò¢¨yo@ êÆ§quot; ±j êÆÔnû!
33. 33. VØ êÆ[êÆÔn ²;ÔnêÆ CÔnêÆ yÔnêÆ ðd§ ðdÄuêÆþ{'Ä '§ÐÔnÆ[ '½ÆØÎ§ 5y²´ÔnÆ[á quot; ðdl¦'§Ñ b^Å'ýóÚIb^Å'ß § 5Ñ ¢¨y¢quot; e¡o§yQ¡ðd§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 ðd§^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 ÷vÅÄ§, ddÑb^Å'ýóquot; ±j êÆÔnû!
35. 35. VØ êÆ[êÆÔn ²;ÔnêÆ CÔnêÆ yÔnêÆ ðd§dÂéØ ðd§'ïÄ',­@t´dÂéØquot; {.I(Faraday) I'DÂ'H'±'V gquot; ðd5¿ Xt±´'½'§QØÓ'ëìXeI ØÓquot; ùðÖ(Michelson)'Í¶¢¨ØÎquot; ±j êÆÔnû!
36. 36. VØ êÆ[êÆÔn ²;ÔnêÆ CÔnêÆ yÔnêÆ ðd§dÂéØ âÔ[(Lorentz)ÚOÏdquot;(Einstein) ´QdÄ:þuÐ dÂéØ§Ñ 5'Bquot; DÅdÄ(Minkowski)Ñ'êÆAº^ Sê¥ Sg'VgµmÚm¨¤omµ R4 = {(t, x, y, z) : t, x, y, z ∈ R}, ØÓëìXm'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 ðd§5|Ø ðdQí¦'§§^ 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'´PÂéØ!þfåÆÚS| Øquot; §^ þ­VkuÐ'xõêÆ©|µ©AÛ!ÿ ÀÆ!v«Ø1quot; ±j êÆÔnû!
39. 39. VØ êÆ[êÆÔn ²;ÔnêÆ CÔnêÆ yÔnêÆ 2ÂéØ±c©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; ù®Ñy ChristoffelÎÒ1quot; ±j êÆÔnû!
40. 40. VØ êÆ[êÆÔn ²;ÔnêÆ CÔnêÆ yÔnêÆ 2ÂéØ©AÛ iùAÛ'A^´Einstein£OÏdquot;¤Má'PÂ éØquot; PÂéØÑuX´^­LorentzÝþ'6G5£ã §Einstein§òAÛþ(Ricci­Ç¤Ônþ£Uþ¨Ä þÜþ¤éXå5quot; êÆ[FËA(Hilbert)^g©{íÑ ý¥ 'Einstein§§¢¦gC`vk=êÆ[± OEinsteinquot; ±j êÆÔnû!
41. 41. VØ êÆ[êÆÔn ²;ÔnêÆ CÔnêÆ yÔnêÆ 2ÂéØ¢¨yâ PÂéØ'k±eýóµY@Y#'cÄ!I'­! çÉ'Q!ÚåÅ11quot; Y@Y#'cÄQPÂéØJÑ±cÒB© quot; PÂéØJÑØÈ§u) gF quot;Bÿ¢|Bÿ IQNg'­quot; ¨Æ)¯¦µXtvk y¢§¦¬xo`quot;OÏd quot;£µ/@o§·ÐO'þPa ¢Ãquot;ÃØX Û§ùnØ´ ('quot;0 ±j êÆÔnû!
42. 42. VØ êÆ[êÆÔn ²;ÔnêÆ CÔnêÆ yÔnêÆ 2ÂéØ¢¨yâ çÉkéõBÿyâquot;k'´HawkingÚPenrose^ ©ÿÀÆØyçÉ'QSquot; PÂéØ'­íØ´Ä'»Fµ»´Aä ½Â 'quot;ùdwÇ(Hubble)'Bÿ¤|±quot; d9'k»'¿åFquot;ùF'ýó ´»¥QµË§ù®Bÿ quot; ÚåÅ'Bÿ´¨V­'8quot; ±j êÆÔnû!
45. 45. VØ êÆ[êÆÔn ²;ÔnêÆ CÔnêÆ yÔnêÆ k)y©AÛ k)'óPK ©AÛ!êAÛ!êêØ! êÿÀ1õ+quot; ¦'óµd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 Cartanaq§£¤Ðk)k)~97 ÔnÆquot; ¦¼Fieldsø'üóÑEinsteink9µ´PÂ éØ¥' þß§´9uKahler-EinsteinÝþ ¨ 'Calabißquot; XtEinsteiné¦!{¬´o\$'|µ§U¢· 'åu quot; ±j êÆÔnû!
47. 47. VØ êÆ[êÆÔn ²;ÔnêÆ CÔnêÆ yÔnêÆ þfnØVÇØ þ­VÊc±cPÂéØ|{'´þfåÆquot; EinsteinA¢ïá PÂéØ'nØe¨Ø Ó§þfåÆ´QxõÔnÆ['¡ÓãåeuÐå5'§ Ùv§¥kxõ¹¢ÚØquot; ~X§QþfåÆ¥éÔ6Äæ^ aq9åÆ¥'VÇ Aºquot; ,Einstein)éIb¨A'Aº¦¦¤þfnØ'M ©§¦éBrown6Äv­ïÄ§¦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'8þPf¯ íº0À£¹#µ/·ØUþPTxo0 Einstein¨céþfåÆ'¦¤ yQþf8EÆ' ÑuX§Qù+gc5k¢¨§X¢ïë' ¢¨quot; ùpJ ù´ rx±eêÆÚÔn'ØÓµ¢¨´u ¨ÔnnØ'ªsOquot;·¬w vknØ'kI? Ø§k¢¨Ãlåquot; ±j êÆÔnû!
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