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1 -Goldstone ( )
2 様々な物理状態 自発的対称性の破れ 並進対称性 U(1)ゲージ対称性 並進対称性 CC by-sa Didier Descouens ガリレイ対称性 CC by-sa Mai-Linh Doan CC by-sa Roger McLassus 並進対称性 スピン対称性 カイラル対称性 CC by-sa Aney SU(2)xU(1) ゲージ対称性 CC by-sa Elijah van der Giessen 多くの場合波をともなう
3 CC by-sa Cburnett 180,x,y y.
4 ,,,, U(1)xSU(2)xSU(3)
5 Noether 1915 U(1)
6 ,... ( )
7 , CP,...,...
8 : (1900~) Magnetic domain Weiss (1907) Ising Lenz (1920) Ising (1925) Heisenberg Bloch Heisenberg (1928) Bloch (1930) NG Onnes (1911) BCS, Goldstone ( ) Brout-Englert-Higgs Bardeen, Cooper, Schrieffer ( 57) Nambu( 60), Goldstone (61), Nambu, Jona-Lasinio ( 61), Goldstone, Salam, Weinberg ( 62). Anderson( 62), Brout, Englert ( 64), Higgs ( 64), Guralnik, Hagen, Kibble ( 64), Migdal, Polyakov ( 65)
9 Qa h[q a, i(x)]i tr [Q a, i(x)] 6= 0 Φi : = ih : = exp( (H µn)) tr exp( (H µn))
10 ,... Bloch T 3/2 Debye T 3, r , from Kittel and Kroemer (1980) o (T/T c )3/2 Holtzberg, McGuire, M'ethfessel, Suits, J. Appl. Phys. 35,1033 (1964)
11 F [ ] F [ ]
12 a
13 = -Goldstone(NG) Nambu( 60), Goldstone(61), Nambu, Jona-Lasinio( 61), ( ) ( )
14 -Goldstone Goldstone, Salam, Weinberg( 62) Lorentz =NG
15 NG : ( ) SU(2) L SU(2) R! SU(2) V F [ ] 3 : NG : +,, 0 :! = p k 2 + m 2
16 NG : ( ) : He4 ( ) :.
17 NG Nielsen - Chadha( 76) N type-i +2N type-ii N BS Type-I:! / k 2n+1 Type-II:! / k 2n Schafer, Son, Stephanov, Toublan, and Verbaarschot ( 01) h[q N NG = N a,q b ]i =0 BS Watanabe - Brauner ( 11) N BS N NG 1 2 rank [Q a,q b ]
18 Watanabe, Murayama ( 12) YH ( 12) N BS N NG = 1 2 rankh[q a,q b ]i N type-i +2N type-ii = N BS N type-ii = 1 2 rankh[q a,q b ]i
19 Watanabe, Murayama ( 12) YH ( 12) N BS N NG = 1 2 rankh[q a,q b ]i
20 2 Type-A Type-B! p g! g
21 Type-A Type-B z x, y 2
22 Type-A, Type-B
23 Type-A, Type-B 1 {L x,l y } P = L z 6=0
24 Watanabe, Murayama ( 12), YH ( 12) NG 2 : Type-A Type-B N type-a = N BS 2N type-b N BS N NG = 1 2 rankh[q a,q b ]i
25 NG ) cf. Nambu ( 04)
26 Type-A (B) Type-I (II) NG Type-A NG Type-B NG Hayata, YH, Hirono (14) Type-A = Type-I ( Watanabe, Murayama ( 12))) Hayata, YH, Hirono (14) Type-B = Type-II
27 Type-B NG 1 N BS N type-i N type-a type-ii type-b b ]in BS N 2 rankh[q a,q b ]i N type-a +2N type-b NG Spin wave in ferromanget O(3) O(2) NG modes in Kaon condensed CFL SU(2)xSU(1) Kelvin waves in vortex translation nonrelativistic massive C U(1)x N type-a +2N type-b = N BS N BS N NG = 1 2 rankh[q a,q b ]i
![[010] [100] x y](/docs-images/94/121717064/images/28-2.jpg "topological number")
28 c ) 2+1D skyrmion [P x,p y ] / N [010] [100] x y topological number ) domain wall in nonrelativistic massive CP 1 model [P z,q] / N z U(1) topological number
29 + NG Type-A:! p h ) Type-B:! h ). Nicolis, Piazza ( 12), ( 13) Watanabe, Brauner, Murayama ( 13)
30
31 1 (3 ) (3 ) (3 )., NG 3.
32 2 : : h (x)i h[p x, ]i = i@ x h i6=0 Low - Manohar y Low, and Manohar ( 02) L z : h[l z, ]i = iy@ x h i6=0 2 NG x string h (x)i P x
33 : O(3) O(2) -A O(3) O(2)
34 Inverse Higgs mechanism Low, Manohar ( 02) Watanabe, Brauner ( 14) = e ixµ P µ e it a a (x) = i 1 d = ie it a a (d + ip µ dx µ )e it a a = P µ dx µ +[T a,ip µ dx µ + d]+ = P µ dx µ + T a (@ µ a + fµ ba b )dx µ + Hayata, YH ( 14) Inverse Higgs mechanism F [ ]
35 ) (Type-A) : N BS = N EV =2 O(3) O(2) L i (x) = ijk x j T 0k (x) i =1, 2 :! = ak 2 + ibk 2 Hosino, Nakano( 82) ( ) a =0, ) (Type-B?) 1 V h[p z,n]i 6=0! k 3/2
36 SSB + h[q a,q b ]i N BS N NG = 1 2 rankh[q a,q b ]i N type-a +2N type-b = N BS N type-b = 1 2 rankh[q a,q b ]i Type-A (Type-I): Type-B (Type-II):! = ak + ibk 2! = ak 2 + ibk 4
37 : (Inverse Higgs )
熱場
-Goldstone ( ) 様々な物理状態 自発的対称性の破れ 並進対称性 U(1)ゲージ対称性 並進対称性 CC by-sa Didier Descouens ガリレイ対称性 CC by-sa Mai-Linh Doan 並進対称性 スピン対称性 CC by-sa Roger McLassus カイラル対称性 CC by-sa Aney CC by-sa Elijah van der Giessen
橋本研
-Goldstone ( ) 2011 4-2012 3 -Goldstone UV IR SSB+ : Chiral Lagrangian :,... -Goldstone Nambu( 60), Goldstone(61), Nambu, Jona-Lasinio( 61), Goldstone, Salam, Weinberg( 62) Lorentz ( ) = NG 2002~2004?
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F [ ] F [ ] Nambu( 60), Goldstone(61), Nambu Jona-Lasinio( 61), Goldstone, Salam, Weinberg( 62). N NG = N BS NG : CC by-sa Aney CC by Zouavman Le Zouave CC by-sa Roger McLassus U(1) CC by-sa Aney -Goldstone
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