The Heat Kernel in Riemann Normal Coordinates and Multiloop Feynman Graphs in Curved Spacetime

TL;DR

This paper develops a formalism using the heat kernel method to compute multi-loop Feynman graphs in curved spacetime, specifically calculating off-diagonal heat kernel components in Riemann normal coordinates up to second order in curvature.

Contribution

It introduces a novel approach for evaluating complex Feynman graphs in curved spacetime by explicitly computing heat kernel components in Riemann normal coordinates.

Findings

Derived off-diagonal heat kernel components up to second order in curvature.

Provided a systematic method for multi-loop Feynman graph calculations in curved backgrounds.

Enhanced the computational toolkit for quantum field theory in curved spacetime.

Abstract

We present a formalism for computing arbitrary multi-loop Feynman graphs in curved spacetime using the heat kernel approach. To this end, we compute the off-diagonal components of the heat kernel in Riemann normal coordinates up to second order in the curvature.