Nonperturbative Aspects of Quantum Field Theory in Curved Spacetime

TL;DR

This paper explores nonperturbative quantum effects in curved spacetime using the functional renormalization group, focusing on an Unruh--DeWitt detector model and providing pedagogical reviews of related quantum field theory and renormalization techniques.

Contribution

It introduces a nonperturbative approach to quantum field theory in curved spacetime via the functional renormalization group and offers comprehensive pedagogical reviews of the algebraic approach and Wetterich equation.

Findings

Divergences occur when the detector's energy gap approaches zero.

Formulation of the detector system in terms of an action for RG analysis.

Discussion of potential methods to address divergences.

Abstract

Quantum field theory in curved spacetime is perhaps the most reliable framework in which one can investigate quantum effects in the presence of strong gravitational fields. Nevertheless, it is often studied by means of perturbative treatments. In this thesis, we aim at using the functional renormalization group -- a nonperturbative realization of the renormalization group -- as a technique to describe nonperturbative quantum phenomena in curved spacetimes. The chosen system is an Unruh--DeWitt particle detector coupled to a scalar quantum field. We discuss how to formulate such a system in terms of an action and how one can compute its renormalization group flow in the case of an inertial detector in flat spacetime, for simplicity. We learn, however, that the results are divergent in the limit in which the detector's energy gap vanishes. Possible workarounds are discussed at the end. This thesis also presents a review of quantum field theory in curved spacetimes by means of the algebraic approach, although it assumes no previous experience with functional analysis. Hence, it fills a pedagogical gap in the literature. Furthermore, we also review the functional renormalization group and derive the Wetterich equation assuming a general field content that might include both bosonic and fermionic fields. Such a derivation is also hardly found in pedagogical introductions available in the high energy physics literature.