Path integrals and degrees of freedom in many-body systems and relativistic field theories

TL;DR

This paper reviews methods to clarify physical degrees of freedom in path integral formulations of many-body and relativistic field theories, aiding in constraints and approximations.

Contribution

It introduces a systematic approach to derive path integrals from operator forms after identifying physical degrees of freedom.

Findings

Enhanced understanding of degrees of freedom in path integrals

Improved techniques for imposing constraints in path integral formalism

Facilitated approximations in complex quantum systems

Abstract

The identification of physical degrees of freedom is sometimes obscured in the path integral formalism, and this makes it difficult to impose some constraints or to do some approximations. I review a number of cases where the difficulty is overcame by deriving the path integral from the operator form of the partition function after such identification has been made.