Contents 3.2 Field operators for bosons 3.2.1 3.2.2 of field opetator Hamilto nian int 3.2.3 Why second quantization? 170224 34 Second quantization for fermions 3.4.1 Creation and annihilation operators for fermions 3.4.2 Field operators 3.5 Summary of second quantization Exercises 15870888 Solutions PART II EXAMPLES 4 Magnetism 90 4.1 Non-interacting Fermi gas 4.2 Magnetic ground state 4.2.1 Trial wave function 4.3 Ene Kinetic energy 32 Potential energy 4.3.3 Energy balance and phases 4.4 Broken symmetry 4.5 Excitations in ferromagnetic metals Single-part e excitations Electron-hole pairs Magnons 99999999991010161910 45.4 Magnon spectrum Exercises Solutions 5 Superconductivity 5.1 Attractive interaction and Cooper pairs 5.1.1 Trial wave function 5.12 Nambu boxes 5.2 Energy minimization 5.3 Particles and quasiparticles 5.4 Broken symmetry Exercises Solutions 6 Superfluidity 6.1 Non-interacting Bose gasvi Contents 3.2 Field operators for bosons 66 3.2.1 Operators in terms of field operators 67 3.2.2 Hamiltonian in terms of field operators 70 3.2.3 Field operators in the Heisenberg picture 72 3.3 Why second quantization? 72 3.4 Second quantization for fermions 74 3.4.1 Creation and annihilation operators for fermions 75 3.4.2 Field operators 78 3.5 Summary of second quantization 79 Exercises 82 Solutions 83 PART II EXAMPLES 87 4 Magnetism 90 4.1 Non-interacting Fermi gas 90 4.2 Magnetic ground state 92 4.2.1 Trial wave function 92 4.3 Energy 93 4.3.1 Kinetic energy 93 4.3.2 Potential energy 94 4.3.3 Energy balance and phases 97 4.4 Broken symmetry 98 4.5 Excitations in ferromagnetic metals 99 4.5.1 Single-particle excitations 99 4.5.2 Electron–hole pairs 102 4.5.3 Magnons 103 4.5.4 Magnon spectrum 105 Exercises 109 Solutions 110 5 Superconductivity 113 5.1 Attractive interaction and Cooper pairs 114 5.1.1 Trial wave function 116 5.1.2 Nambu boxes 118 5.2 Energy 119 5.2.1 Energy minimization 120 5.3 Particles and quasiparticles 123 5.4 Broken symmetry 125 Exercises 128 Solutions 132 6 Superfluidity 135 6.1 Non-interacting Bose gas 135