Properties of the thermal two-point functions in curved spacetimes for a self-interacting scalar field

TL;DR

This paper develops a method to construct a consistent algebraic quantum field theory for a self-interacting massive scalar field in Schwarzschild spacetime, focusing on thermal states and their two-point functions.

Contribution

It extends flat spacetime AQFT methods to curved Schwarzschild spacetime for interacting fields, analyzing thermal two-point functions and their asymptotic properties.

Findings

Constructed a consistent AQFT framework in Schwarzschild spacetime.

Analyzed asymptotic properties of thermal two-point functions.

Achieved finite expectation values for observables in the interacting theory.

Abstract

We will present a method for building a consistent AQFT on Schwarzschild spacetime for a thermal system ruled by an interacting and massive scalar field, extending the methods and the results of K. Fredenhagen and F. Lindner valid for the flat case. In particular we will discuss the asymptotic properties of the two-point function of a thermal (KMS) state in order to obtain finite expectation values for the observables of the theory.