Derivative expansion of quadratic operators in a general 't Hooft gauge

TL;DR

This paper introduces a derivative expansion method for calculating functional determinants of quadratic operators in 't Hooft gauges, facilitating complex gauge-fixed Lagrangian analyses.

Contribution

It develops a novel derivative expansion technique specifically for non-diagonal quadratic operators in gauge theories, expanding computational tools in quantum field theory.

Findings

Effective computation of functional determinants in complex gauge settings.

Application of the method to various gauge-fixed Lagrangians.

Enhanced understanding of quadratic operator structures in gauge theories.

Abstract

A derivative expansion technique is developed to compute functional determinants of quadratic operators, non diagonal in spacetime indices. This kind of operators arise in general 't Hooft gauge fixed Lagrangians. Elaborate applications of the developed derivative expansion are presented.