1. 1.1....................... 1.2............................ 1.3.................... 1.4.................. 2. 2.1.................... 2.2..................... 2.3.................... 3. 3.1..................... 3.2................ 3.3 RKKY........ 3.4.................. 3.4 s-d...................... 3.5.................. 3.6 QCD................................ 3.7....................... 3.8....................... 3.9...... 1

4. 4.1 -................. 4.2....................... 4.3....................... 4.4..................... 4.5...................... 4.5a....................... 4.5b......................... 4.5c...... 4.5d............... 4.6....................... 4.7......................... 5. 5.1 φ 4............................... 5.2 XY -............ 5.3 -............. 5.4...................... 5.5 Ward-Takahashi.................... 5.6.............................. 6. 6.1............... 6.2................ 6.3......................... 6.4..................... 7. 7.1 BCS............................. 7.2................ 7.3......................... 7.4 Nambu-Jona-Lasinio................... 7.5 -................... 8. 8.1............................ 8.2..................... 2

8.3................. 9. 9.1.................. 9.2................. 9.3.................... 9.4.......................... 3

1 1.1 1761 Euler Principia motus fluidorum 1864 Maxwell Electromagnetic field 1900 Planck 12 14 1904 Lorentz Lorentz 1905 Einstein Special Relativity 1908 Minkowski Raum und Zeit 1911 Kamerlingh Onnes Hg T c = 4.2K 1915 Einstein Allgemeine Relativitästheorie 1925 Heisenberg 1926 Schrödinger Wellenmechanik 1826 Dirac Dirac 1927 Dirac Maxwell field 1927 Bloch 1928 Jordan-Wigner 1929 Heisenberg-Pauli 1930 1932 C. D. Anderson 1933 Meissner-Ochsenfeld Meissner 1933 de Haas, de Boer, van den Berg 1934 Pauli-Weisscopf 1934 Fermi 1935 1937 Kapitsa T c = 2.17K 1940 Pauli 1943 Heisenberg S 1943 1945 ESR NMR 1949 Tomonaga, Schwinger, Feynman, Dyson 1954 Yang-Mills 4

1955 S 1957 BCS 1958 Landau 1960 Josephson 1960 1964 Gell-Mann, Zwig 1964 1971 K. G. Wilson 1972 Osheroff, Richardson, Lee T c = 2.6mK 1973 Kosterlitz-Thouless 1974 Gross, WIlczek, Politzer 1979 Anderson 1980 1983 STM Scanning Tunneling Microscopy 1986 Bednorz, Muller 1995 87 Rb 2004 40 K 6 Li 100nK 5

1.2 L L L h2 2m 2 ψ = ɛψ. (1) ψ = 1 V e ik r (2) ψ(x + L, y, z) = ψ(x, y + L, z) = ψ(x, y, z + L) = ψ(x, y, z) (3) k x = 2π L n x, k y = 2π L n y, k z = 2π L n z. (4) n x n y n z C T C = 2 π2 π 2 k 3 k2 B 2 Bρ(ɛ F )T = N e h 2 mt (5) kf 2 1000 1000 3R/2 1.3 6

k k k 1 1.4 1. 2. P.W. Anderson Basic Notions of Condensed Matter Physics 1. H H = kσ ɛ k c kσ c kσ g kk c k c k c k c k, (6) 7

BCS BCS ψ = k (u k + v k c k c k ) 0 (7) -BCS 11(1976)297 2. QED 2 2.1 ev 8

ɛ F ev (8) e2 d ev (9) - W = 1/τ T 2 1 τ (k BT ) 2 k B T, (10) ɛ F Fermi liquid theory 1/τ H = kσ ɛ k c kσ c kσ + U 1 N c k q c k +q c k c k. (11) kk q ImΣ R k (ɛ) = U 2 q ImG R k q(ɛ ) k dɛ ( coth ɛ ɛ 2π 2k B T ( dx 2π ) ɛ tanh 2k B T tanh x k B T tanhx + ɛ ɛ 2k B T ImG R k (x)imgr k +q(x + ɛ ɛ ) (12) ) 9

Table 1: Green z ρ ImΣ ReΣ z ρ d = 1 T or ɛ ɛ ln ɛ z = 0 T d = 2 T 2 ln T or ɛ 2 ln ɛ ɛ z 0 T 2 ln T d = 3 T 2 or ɛ 2 ɛ z 0 T 2 G R k (ɛ) Green ɛ = 0 dɛ ( coth ɛ 2k B T ) ɛ tanh F (ɛ ) = F (0)(πk B T ) 2 (13) 2k B T ImΣ R k (0) = 1 2π U 2 (πk B T ) 2 1 dx 2k B T cosh 2 (x/2k B T ) ImG R k q(0)img R k (x)imgr k +q(x) (14) k q 3 ImΣ R k (0) T 2 (15) ImΣ R k (ɛ) ɛ 2 (T = 0) (16) T 2 1 1. I,II. 2. II. 3. A. A. Abrikosov, L. P. Gorkov, I. Ye Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics. 4. K. Nishijima, Fields and Particles (1969). 5. N. N. Bogoliubov, D. V. Shirkov, Introduction to the Theory of Quantized 10

Fields. 6.. 7. C. Hodges, H. Smith and J. W. Wilkins, Phys. Rev. B34, 302 (1971). 8. P. Bloom, Phys. Rev. B12, 125 (1975). 11