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

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