Stochastic quantization of scalar fields in Einstein and Rindler spacetime

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 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.

Stochastic quantization of scalar fields in de Sitter spacetime

“…In the development of this program some authors applied this method to linearized Euclidean gravity [6] [7] and also non-linearized gravity. We may observe, as it was remarked earlier [8], that the study of a situation which lies between these two extremes is missing. A consistent logical step is to discuss an intermediate situation between fields in flat spacetime and quantum gravity, i.e., the semiclassical theory [9] [10].…”

“…We defined the retarded Green function for the diffusion problem in the Eq. (8). Let us assume that the coupling constant is a small quantity.…”

“…The stochastic quantization method was used recently to study self-interacting scalar fields in manifolds which can be analytically continued to the Euclidean situation, i.e. the Einstein and the Rindler space [8]. First, the authors solved a Langevin equation for the mode coefficients of the field and then exhibited the two-point correlation function at the one-loop level.…”

Stochastic quantization of real-time thermal field theory

“…Recently, the stochastic quantization for fields defined in a curved spacetime have been studied in the Refs. [8] [9]. Nevertheless, for non-static curved manifolds we have to extend the formalism beyond the Euclidean signature, i.e., to formulate the stochastic quantization in pseudo-Riemannian manifold, instead of formulating it in the Riemannian space, as was originally proposed.…”

Stochastic quantization for complex actions

“…[5]. Recently Menezes and Svaiter [6] implemented the stochastic quantization in the theory of self-interacting scalar fields in a static Riemannian manifold and also a manifold with a event horizon, namely, the Einstein and the Rindler manifold. First, these authors solved a Langevin equation for the mode coefficients of the field, then they exhibit the two-point function at the one-loop level.…”