The split property for quantum field theories in flat and curved spacetimes

TL;DR

This paper reviews the split property in algebraic quantum field theory, discussing its proof in flat and curved spacetimes, and explores its connections to nuclearity and quantum energy inequalities.

Contribution

It provides an expository account of nuclearity and the split property, and outlines a recent proof of the split property in curved spacetimes.

Findings

Split property holds under nuclearity in Minkowski spacetime.

Recent proof of split property in curved spacetimes.

Connections established between split property, nuclearity, and quantum energy inequalities.

Abstract

The split property expresses a strong form of independence of spacelike separated regions in algebraic quantum field theory. In Minkowski spacetime, it can be proved under hypotheses of nuclearity. An expository account is given of nuclearity and the split property, and connections are drawn to the theory of quantum energy inequalities. In addition, a recent proof of the split property for quantum field theory in curved spacetimes is outlined, emphasising the essential ideas.