Locally covariant quantum field theory and the problem of formulating the same physics in all spacetimes

TL;DR

This paper explores the framework of locally covariant quantum field theory, using functors to represent theories and natural isomorphisms to express their physical equivalence across different spacetimes, addressing foundational issues and the concept of dynamical locality.

Contribution

It introduces a functorial approach to locally covariant quantum field theories, clarifies the notion of dynamical locality, and discusses implications for representing physics consistently in all spacetimes.

Findings

Theories can be represented by functors with physical equivalence via natural isomorphisms.

Two definitions of local physical content are proposed, with their coincidence defining dynamical locality.

Dynamical locality has implications for understanding the same physics in different spacetimes and for the existence of natural states.

Abstract

The framework of locally covariant quantum field theory is discussed, motivated in part using "ignorance principles". It is shown how theories can be represented by suitable functors, so that physical equivalence of theories may be expressed via natural isomorphisms between the corresponding functors. The inhomogeneous scalar field is used to illustrate the ideas. It is argued that there are two reasonable definitions of the local physical content associated with a locally covariant theory; when these coincide, the theory is said to be dynamically local. The status of the dynamical locality condition is reviewed, as are its applications in relation to (a) the foundational question of what it means for a theory to represent the same physics in different spacetimes, and (b) a no-go result on the existence of natural states.