Functional Integral Techniques in Condensed Matter Physics

Jaime Merino, A. Levy Yeyati

R. Vilela Mendes

A. B. Balantekin

Bernhard Mühlschlegel

G. Fletcher

As an example of the application of functional integral techniques to condensed matter physics, the partition function for the BCS model for superconductivity is derived. The pairing term in the Hamiltonian is linearized by applying the Hubbard–Stratonovich transformation. It is shown that the standard result for the gap equation can be obtained by making a saddle-point approximation to the functional integral.

Alexander Altland, Benjamin D. Simons

Modern experimental developments in condensed matter and ultracold atom physics present formidable challenges to theorists. This book provides a pedagogical introduction to quantum field theory in many-particle physics, emphasizing the applicability of the formalism to concrete problems. This second edition contains two new chapters developing path integral approaches to classical and quantum nonequilibrium phenomena. Other chapters cover a range of topics, from the introduction of many-body techniques and functional integration, to renormalization group methods, the theory of response functions, and topology. Conceptual aspects and formal methodology are emphasized, but the discussion focuses on practical experimental applications drawn largely from condensed matter physics and neighboring fields. Extended and challenging problems with fully worked solutions provide a bridge between formal manipulations and research-oriented thinking. Aimed at elevating graduate students to a level where they can engage in independent research, this book complements graduate level courses on many-particle theory.