Heat Kernel Methods for Multiloop Calculations in Curved Spacetime: Nonzero Spin

TL;DR

This paper extends heat kernel techniques for multiloop Feynman diagram calculations in curved spacetime to include spin-$rac{1}{2}$ fermions, broadening the applicability of the formalism.

Contribution

It introduces a method to incorporate spinor fields into the heat kernel framework for multiloop calculations in curved spacetime.

Findings

Extended heat kernel formalism to spin-$rac{1}{2}$ fields.

Demonstrated applicability to fermionic fields in curved backgrounds.

Provided groundwork for future multiloop fermionic calculations.

Abstract

In a previous paper we have presented a general formalism for computing Feynman diagrams for scalar fields in curved spacetime at any loop order using heat kernel methods. The main technique used is the expansion of the fully off-diagonal heat kernel in Riemann normal coordinates. In this work we extend this to include fields of nonzero spin, in particular spin-$\frac{1}{2}$ fermions.