Condensed Matter Field TheoryOver the past few decades, in concert with ground-breaking experimental advances, condensed matter theory has drawn increasingly from the language of low-energy quantum field theory. This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. It emphasizes the development of modern methods of classical and quantum field theory with applications oriented around condensed matter physics. Topics covered include second quantization, path and functional field integration, mean-field theory and collective phenomena, the renormalization group, and topology. Conceptual aspects and formal methodology are emphasized, but the discussion is rooted firmly in practical experimental application. As well as routine exercises, the text includes extended and challenging problems, with fully worked solutions, designed to provide a bridge between formal manipulations and research-oriented thinking. This book will complement graduate level courses on theoretical quantum condensed matter physics. |
Contents
Preface page vii | 3 |
Second quantization | 39 |
Feynman path integral | 94 |
Functional field integral | 157 |
Common terms and phrases
action analysis appear application approach approximation assume becomes behavior bosonic chapter charge classical compute condition conductance configuration consider constant contribution coordinate correlation function coupling critical defined definition denotes density dependence derivative described developed diagrams dimension discussion effective electron energy equation example excitations exercise expansion expectation explore expression fact factor Fermi fermion field theory figure fixed fluctuations formulation frequency gauge given Green function ground Hamiltonian identify implies important interaction introduced invariant leads limit magnetic matter mechanics mode momentum Notice observed obtain operator parameter particle path integral perturbation phase physics potential present problem quantum quantum mechanics reference relation representation represents response result scaling scattering solution space spin structure symmetry takes temperature topological transformation transition turn vector