The Schwinger-DeWitt technique in Gauge-Gravity Theories

TL;DR

This paper develops a covariant one-loop effective action using the heat kernel method for gauge and gravity theories, providing new insights into non-local effects and simplifying beta function calculations.

Contribution

It introduces a heat kernel approach for gauge-gravity theories that preserves covariance and computes non-local terms exactly, advancing quantum field theory techniques.

Findings

Exact computation of non-local terms in Yang-Mills theory

Simplified derivation of the Yang-Mills beta function

Discussion on extending the method to quantum gravity

Abstract

We construct the one-loop effective action in Yang-Mills and Pure Quantum Gravity theories with heat kernel(or proper time method), which maintains manifest covariance during and after quantization (gauge and diffeomorphism invariance are always preserved). In this talk, we will basically focus on "What, How, and Why" we prefer heat kernel than the standard Feynman diagram calculation in momentum space at the one loop correction. The beta function of Yang-Mills field in the fixed gravitational background can be more simply obtained. The non-local term which cannot be easily obtained in the expansion method are exactly computed in Yang-Mills in the case of covariantly constant background field. The local term is consistent with asymptotic expansion method or any most standard method. The non-local terms give some physical implication concerning non-perturbative problems such as confinement and instabilities. The modification of this technique to quantum gravity is discussed.