Alternative dimensional reduction via the density matrix: A test

TL;DR

This paper explores an alternative approach to dimensional reduction using the density matrix, analyzing the perturbation series for classical effective actions in quantum statistical mechanics as a simplified model for quantum field theory at finite temperature.

Contribution

It introduces a novel method for dimensional reduction via the density matrix and computes initial terms of the perturbation series for specific potentials.

Findings

Perturbation series derived for harmonic oscillator and quartic potential.

Analysis provides insights into effective actions in quantum statistical mechanics.

Method offers a new perspective for finite temperature quantum field theory.

Abstract

We derive and analyze the perturbation series for the classical effective action in quantum statistical mechanics, treated as a toy model for the dimensionally reduced effective action in quantum field theory at finite temperature. The first few terms of the series are computed for the harmonic oscillator and the quartic potential.