规范变化与规范不变.pdf

CHAPTER 2. íP(5¡:-Ñ–® 6 2.2 ƒ⇤ÿb ƒ⇤ ÿ ƒ⇤ÿb(gauge tranform)⇢ ~!A ~0 = A ~ + r⇤ A @⇤ ! 0= c@t (2.19) (2.20) E, B: ÿ F/‚˝p⇢ ⇢9ÿ Ô¡ , Çú (r, t)/õöπ↵(2.12)Ñ„ ! /ÿb (2.12)Ñ„ ¡ ⇢ 0 £H q⇤ = ei ~c (2.21) sÍÓ *¯‡P. iq⇤ @ iq⇤ q@⇤ 0 @ (e ~c ) = + e ~c i~ @t c@t @t iq⇤ q ~0 0 q~ ( i~r A ) = e ~c ( i~r A) c c iq⇤ q ~0 2 0 q~ 2 ( i~r A) = e ~c ( i~r A) c c iq⇤ @⇤ q 0 0 = e ~c (q ) c@t i~ ‡d i~ @ iq⇤ 1 (e ~c ) = [ ( i~r @t 2µ (2.22) (2.23) (2.24) (2.25) q⇤ q ~0 2 A ) + q 0 ]ei ~c c (2.26) ƒ⇤ÿb}69ÿÜ‚˝p F/ • 9ÿ‚˝pчᄠ(1) ⇢ ÿ (2) )((2.18), π◆¡ j0 = ⇢ q⇤ (r(S + ) µ c • }6Ÿ*¯‡P/MnÑ˝p <˝ ø. F/Ô¡ üeÑ‚˝ph: )( sÔ¡ ⇧ƒ⇤ ÿ. Â⌦ÔÂ(‘ƒ⇤ Z d3 x~j = q (A + r⇤) = j c h(P P⌥å ®œÑ *i⌃∂ ⇥ qA c )i µ = h⇧i µ ÿ(gauge invariant)’e;”⇥ ↵b⌘Ïe\Ù ,Ñœ. :∞ (2.27) (2.28) 2.2. ƒ⇤ÿb ƒ⇤ ÿ 7 Ô‰ÿbM :|↵i, ÿb :|↵0 i. æ |↵0 i = G|↵i (2.29) h↵|↵i = h↵0 |↵0 i = 1 (2.30) ñH⌘ÏÅB sM ˝R . Ÿ7Ñÿ ÔÂ⌃„:HilbertzÙœёl®’. Ÿ ÅB G † G = 1, (2.31) sÿb/zcÑ⇥ ÷ у⇤ îÂ9ÿi⌃œÑ <⇥Ÿ1ÅB h↵|G † xG|↵i = h↵|x|↵i (2.32) h↵|G † ⇧0 G|↵i = h↵|⇧|↵i (2.33) G † xG = x (2.34) G † ⇧0 G = ⇧ (2.35) _1/ÅB Gæ G=e iq⇤(x,t) ~c (2.36) 1Ô·≥Â⌦ÅB⇥ 1é[x, G] = 0, Eq.(2.34)/>6Ñ⇥ )([P, G] = i~rG, ⇧0 = P qA0 /c, Ô¡ Eq.(2.35). _1/Ùƒ⇤ÿb¸ÙÑ Ü). ‚œÀl ›¡Ühxi, h⇧i ÿ. ( F/hP iÿ