Correct path-integral formulation of quantum thermal field theory in coherent-state representation

TL;DR

This paper introduces a new path-integral quantization method for thermal quantum fields in the coherent-state representation, providing correct expressions for partition functions and generating functionals for practical analytical calculations.

Contribution

It presents a novel formulation of thermal quantum field theory in the coherent-state representation with explicit derivations for electrodynamics and $$ theory, enabling analytical computations.

Findings

Correct expressions for partition functions obtained

Generating functionals derived in coherent-state representation

Perturbative expansions achieved via stationary-phase method

Abstract

The path-integral quantization of thermal scalar, vector and spinor fields is performed newly in the coherent-state representation. In doing this, we choose the thermal electrodynamics and $\phi ^4$ theory as examples. By this quantization, correct expressions of the partition functions and the generating functionals for the quantum thermal electrodynamics and $\phi ^4$ theory are obtained in the coherent-state representation. These expressions allow us to perform analytical calculations of the partition functions and generating functionals and therefore are useful in practical applications. Especially, the perturbative expansions of the generating functionals are derived specifically by virtue of the stationary-phase method. The generating functionals formulated in the position space are re-derived from the ones given in the coherent-state representation.