Why Does Quantum Field Theory In Curved Spacetime Make Sense? And What Happens To The Algebra of Observables In The Thermodynamic Limit?

TL;DR

This paper provides an accessible overview of quantum field theory in curved spacetime, the thermodynamic limit in quantum statistical mechanics, and their analogs in large N gauge theories, highlighting foundational concepts and results.

Contribution

It offers a non-technical introduction to key results connecting quantum field theory, thermodynamics, and gauge theories, emphasizing their conceptual links.

Findings

Classical results on quantum field theory in curved spacetime explained.

Overview of the thermodynamic limit in quantum statistical mechanics.

Analogies between these results and the large N limit in gauge theories.

Abstract

This article aims to explain some of the basic facts about the questions raised in the title, without the technical details that are available in the literature. We provide a gentle introduction to some rather classical results about quantum field theory in curved spacetime and about the thermodynamic limit of quantum statistical mechanics. We also briefly explain that these results have an analog in the large N limit of gauge theory.