The generalised principle of perturbative agreement and the thermal mass

TL;DR

This paper proves the validity of the Principle of Perturbative Agreement for scalar fields with quadratic interactions and extends the construction of thermal states to massless cases, providing new insights into quantum field theory on curved spacetimes.

Contribution

It develops a new proof of the Principle of Perturbative Agreement for scalar fields with quadratic interactions and extends thermal state constructions to massless scenarios.

Findings

Proof of the Principle of Perturbative Agreement for quadratic interactions

Generalization of the principle to arbitrary quadratic contributions

Extension of thermal state construction to massless scalar fields

Abstract

The Principle of Perturbative Agreement, as introduced by Hollands & Wald, is a renormalisation condition in quantum field theory on curved spacetimes. This principle states that the perturbative and exact constructions of a field theoretic model given by the sum of a free and an exactly tractable interaction Lagrangean should agree. We develop a proof of the validity of this principle in the case of scalar fields and quadratic interactions without derivatives which differs in strategy from the one given by Hollands & Wald for the case of quadratic interactions encoding a change of metric. Thereby we profit from the observation that, in the case of quadratic interactions, the composition of the inverse classical M{\o}ller map and the quantum M{\o}ller map is a contraction exponential of a particular type. Afterwards, we prove a generalisation of the Principle of Perturbative Agreement and show that considering an arbitrary quadratic contribution of a general interaction either as part of the free theory or as part of the perturbation gives equivalent results. Motivated by the thermal mass idea, we use our findings in order to extend the construction of massive interacting thermal equilibrium states in Minkowski spacetime developed by Fredenhagen & Lindner to the massless case. In passing, we also prove a property of the construction of Fredenhagen & Lindner which was conjectured by these authors.