XV Contents 38 Interactions of electrons and phonons in condensed matter 699 38.1 Fermi energy 69 38.2 Interacting electron gas 04 38.3 Phonons 708 38.4 Electron-phonon interaction 713 39 Superconductivity 719 39.1 Many-body system of half-integer spins 719 392 Normal states(△=0.G≠0) 724 39.3 39.4 BCS states(≠0) BCS condensate in Green's function formalism 39.5 Meissner effect 732 39.6 Problems 735 40 Bose-Einstein condensation and superfluidity 736 40.1 Many-body system of integer spins 736 40.2 Superfluidity 740 40.3 Problems 742 % Lagrangian formulation of classical fields 743 41.1 Basic structure 743 41.2 Noether's theorem 744 413 Examples 41.4 Maxwell's equations and consequences of gauge invariance Spontaneous symmetry breaking 7 42.1 BCS mechanism 75 42.2 Ferromagnetism 423 SSB for discrete symmetry in classical field theory 424 SSB for continuous 42.5 Nambu-Golds tone be symm osons 42.6 Higgs mechanism 101016 Basic quantum electrodynamics and Feynman diagrams 43.1 Perturbation theory 43.2 Feynman diagrams 43.3 T(HI (x1)H(x2))and Wick's theorem 777 434 Feynman rules 43.5 Cross-section for 1+23+4 43.6 Basic two-body scattering in QED 786 43.7 QED vs.nonrelativistic limit:electron-electron system 786 43.8 QED vs.nonrelativistic limit:electron-photon system 189 Radiative corrections 793 44.1 Radiative corrections and renormalization 793 xv Contents 38 Interactions of electrons and phonons in condensed matter 699 38.1 Fermi energy 699 38.2 Interacting electron gas 704 38.3 Phonons 708 38.4 Electron–phonon interaction 713 39 Superconductivity 719 39.1 Many-body system of half-integer spins 719 39.2 Normal states ( = 0, G = 0) 724 39.3 BCS states ( = 0) 725 39.4 BCS condensate in Green’s function formalism 727 39.5 Meissner effect 732 39.6 Problems 735 40 Bose–Einstein condensation and superfluidity 736 40.1 Many-body system of integer spins 736 40.2 Superfluidity 740 40.3 Problems 742 41 Lagrangian formulation of classical fields 743 41.1 Basic structure 743 41.2 Noether’s theorem 744 41.3 Examples 746 41.4 Maxwell’s equations and consequences of gauge invariance 750 42 Spontaneous symmetry breaking 755 42.1 BCS mechanism 755 42.2 Ferromagnetism 756 42.3 SSB for discrete symmetry in classical field theory 758 42.4 SSB for continuous symmetry 760 42.5 Nambu–Goldstone bosons 762 42.6 Higgs mechanism 765 43 Basic quantum electrodynamics and Feynman diagrams 770 43.1 Perturbation theory 770 43.2 Feynman diagrams 773 43.3 T(HI (x1) HI (x2)) and Wick’s theorem 777 43.4 Feynman rules 783 43.5 Cross-section for 1 + 2 →3 + 4 783 43.6 Basic two-body scattering in QED 786 43.7 QED vs. nonrelativistic limit: electron–electron system 786 43.8 QED vs. nonrelativistic limit: electron–photon system 789 44 Radiative corrections 793 44.1 Radiative corrections and renormalization 793