Introduction to Thermal Field Theory: From First Principles to Applications

TL;DR

This review introduces the fundamentals of thermal field theory, covering statistical mechanics, quantum fields in media, and applications like particle production and phase transitions, emphasizing path-integral methods and Green's functions.

Contribution

It provides a comprehensive overview of thermal field theory fundamentals and applications, integrating statistical mechanics with relativistic quantum field theory, with detailed methods for computing thermal Green's functions.

Findings

Thermal Green's functions are crucial for understanding particle production.

Phase transitions and vacuum decay are analyzed within thermal field theory.

Path-integral methods effectively compute thermal Green's functions for various fields.

Abstract

This review article provides the basics and discusses some important applications of thermal field theory, namely the combination of statistical mechanics and relativistic quantum field theory. In a first part the fundamentals are covered: the density matrix, the corresponding averages and the treatment of fields of various spin in a medium. A second part is dedicated to the computation of thermal Green's function for scalars, vectors and fermions with path-integral methods. These functions play a crucial role in thermal field theory, as explained here. A more applicative part of the review is dedicated to the production of particles in a medium and to phase transitions in field theory, including the process of vacuum decay in a general theory featuring a first-order phase transition. To understand this review, the reader should only have a good knowledge of non-statistical quantum field theory.