Graviton self-energy from worldlines

TL;DR

This paper reviews worldline methods for calculating the graviton self-energy from various particles and introduces a new approach to compute the graviton's self-energy from itself using a worldline representation of differential operators.

Contribution

It presents a novel application of worldline formalism to compute the graviton self-energy from graviton loops, extending previous methods for particles of spin 0, 1/2, and 1.

Findings

Calculated graviton self-energy from graviton loops using worldline formalism.

Reviewed existing worldline descriptions for particles of different spins.

Proposed a new approach to represent the differential operators in Einstein-Hilbert quadratic approximation.

Abstract

Worldline approaches, when available, often simplify and make more efficient the calculation of various observables in quantum field theories. In this contribution we first review the calculation of the graviton self-energy due to a loop of virtual particles of spin 0, 1/2 and 1, all of which have a well-known worldline description. For the case of the graviton itself, an elegant worldline description is still missing, though one can still describe it by constructing a worldline representation of the differential operators that arise in the quadratic approximation of the Einstein-Hilbert action. We have recently analyzed the latter approach, and we use it here to calculate the one-loop graviton self energy due to the graviton itself in this formalism.