Relativistic Green functions in a plane wave gravitational background

TL;DR

This paper derives exact Green functions for a relativistic particle in a gravitational plane wave background using alternative methods, demonstrating the effectiveness of semiclassical approaches even with non-quadratic Lagrangians.

Contribution

It provides new derivations of Green functions for spinless and spin 1/2 particles in a gravitational wave background using the Fock-Schwinger and algebraic methods.

Findings

Semiclassical approach yields exact Green functions in gravitational plane wave backgrounds.

Alternative derivations confirm previous results by Barducci and Giachetti.

The Lagrangian is non-quadratic but semiclassical methods remain effective.

Abstract

We consider a massive relativistic particle in the background of a gravitational plane wave. The corresponding Green functions for both spinless and spin 1/2 cases, previously computed by A. Barducci and R. Giachetti \cite{Barducci3}, are reobtained here by alternative methods, as for example, the Fock-Schwinger proper-time method and the algebraic method. In analogy to the electromagnetic case, we show that for a gravitational plane wave background a semiclassical approach is also sufficient to provide the exact result, though the lagrangian involved is far from being a quadratic one.