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**Quantum field theory of nonequilibrium states.**
*(English)*
Zbl 1123.82001

Cambridge: Cambridge University Press (ISBN 978-0-521-87499-1/hbk). xiii, 536 p. (2007).

This book is a textbook on the applications of quantum field theory to the analysis of systems in non-equilibrium state. The purpose of the author is two-fold: firstly to thoroughly expand the real-time formalism proposed by Schwinger, and secondly, to provide a broad range of applications, which would emphasize the universality of the approach. The basic tool is the Hamiltonian. The general scheme is to assume that the Hamiltonian at the equilibrium position is perturbed by an additive term and then to work on the latter.

The book comprises twelve almost self-contained chapters: quantum fields, operators on the multi-particle state space, quantum dynamics and Green’s functions, nonequilibrium theory, real-time formalism, linear response theory, quantum kinetic equations, nonequilibrium superconductivity, diagrammatic and generating functionals, effective action (also referred to as effective potential for the theory), disordered conductors, classical statistical dynamics. All these questions are examined on the theoretical point of view, but also by using the intuitive approach provided by Feynman diagrams. The book is complete with a large number of exercises to help the self-study

The book comprises twelve almost self-contained chapters: quantum fields, operators on the multi-particle state space, quantum dynamics and Green’s functions, nonequilibrium theory, real-time formalism, linear response theory, quantum kinetic equations, nonequilibrium superconductivity, diagrammatic and generating functionals, effective action (also referred to as effective potential for the theory), disordered conductors, classical statistical dynamics. All these questions are examined on the theoretical point of view, but also by using the intuitive approach provided by Feynman diagrams. The book is complete with a large number of exercises to help the self-study

Reviewer: Guy Jumarie (Montréal)

### MSC:

82-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistical mechanics |

81-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory |

82C10 | Quantum dynamics and nonequilibrium statistical mechanics (general) |