Worldline formalism in a gravitational background

TL;DR

This paper extends the worldline formalism to include gravitational backgrounds, addressing UV regularization issues and demonstrating its effectiveness in computing one-loop effective actions and graviton self-energies.

Contribution

It provides a first quantized representation of the one-loop effective action in a gravitational background, including explicit calculations of graviton tadpole and self-energy.

Findings

Reproduces results consistent with Feynman diagram calculations

Addresses UV regularization in gravitational worldline formalism

Highlights technical challenges in zero mode factorization

Abstract

We analyze the worldline formalism in the presence of a gravitational background. In the worldline formalism a path integral is used to quantize the worldline coordinates of the particles. Contrary to the simpler cases of scalar and vector backgrounds, external gravity requires a precise definition of the ultraviolet regularization of the path integral. Taking into account the UV regularization, we describe the first quantized representation of the one-loop effective action for a scalar particle. We compute explicitly the contribution to the graviton tadpole and self-energy to test the validity of the method. The results obtained by usual field theoretical Feynman diagrams are reproduced in an efficient way. Finally, we comment on the technical problems related to the factorization of the zero mode from the path integral on the circle.