A momentum-space representation of Feynman propagator in Riemann-Cartan spacetime

TL;DR

This paper develops a momentum-space representation of the Feynman propagator for scalar fields in Riemann-Cartan spacetime, incorporating torsion, and derives related renormalization techniques.

Contribution

It introduces generalized Riemann-normal coordinates based on autoparallels and extends the momentum-space representation of the Feynman propagator to include torsion effects.

Findings

Momentum-space representation generalizes previous Riemannian results.

Derived proper-time representation in Riemann-Cartan spacetime.

Facilitated renormalization of one-loop effective Lagrangians.

Abstract

We first construct generalized Riemann-normal coordinates by using autoparallels, instead of geodesics, in an arbitrary Riemann-Cartan spacetime. With the aid of generalized Riemann-normal coordinates and their associated orthonormal frames, we obtain a momentum-space representation of the Feynman propagator for scalar fields, which is a direct generalization of Bunch and Parker's works to curved spacetime with torsion. We further derive the proper-time representation in $n$ dimensional Riemann-Cartan spacetime from the momentum-space representation. It leads us to obtain the renormalization of one-loop effective Lagrangians of free scalar fields by using dimensional regularization. When torsion tensor vanishes, our resulting momentum-space representation returns to the standard Riemannian results.