Path Integrals in Polar Field Variables in QFT

TL;DR

This paper develops a method to transform Euclidean path integrals from Cartesian to polar field variables, proving the conjecture for general quantum field theory models with two fields.

Contribution

It introduces and proves a conjecture for transforming path integrals into polar variables in quantum field theories with two fields.

Findings

Transformation conjecture verified in toy models

Proof established for general QFT with two fields

Provides a new approach for polar field variable analysis

Abstract

We show how to transform a $d$-dimensional Euclidean path integral in terms of two (Cartesian) fields to a path integral in terms of polar field variables. First we present a conjecture that states how this transformation should be done. Then we show that this conjecture is correct in the case of two toy models. Finally the conjecture will be proven for a general QFT model with two fields.