Stochastic Quantization of Scalar Fields in Einstein and Rindler Spacetime

TL;DR

This paper applies stochastic quantization to scalar fields in curved and flat spacetimes with horizons, calculating two-point functions and addressing divergences with covariant regularization.

Contribution

It introduces a method for stochastic quantization of scalar fields in Einstein and Rindler spacetimes, including regularization of divergences.

Findings

Two-point functions computed up to first order in coupling.

Asymptotic behavior of the two-point function analyzed.

Divergences managed via covariant stochastic regularization.

Abstract

We consider the stochastic quantization method for scalar fields defined in a curved manifold and also in a flat space-time with event horizon. The two-point function associated to a massive self-interacting scalar field is evaluated, up to the first order level in the coupling constant, for the case of an Einstein and also a Rindler Euclidean metric, respectively. Its value for the asymptotic limit of the Markov parameter is exhibited. The divergences therein are taken care of by employing a covariant stochastic regularization.