Stochastic quantization of scalar fields in Einstein and Rindler spacetime

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