A General PCT Theorem for the Operator Product Expansion in Curved Spacetime

TL;DR

This paper establishes a PCT invariance property for the operator product expansion in quantum field theories on general curved spacetimes, extending the concept beyond Minkowski space.

Contribution

It proves a general PCT theorem for the operator product expansion in curved spacetime within an axiomatic framework, replacing the Minkowski spacetime PCT theorem.

Findings

Operator product expansion coefficients are invariant under combined parity, charge, and time reversal.

The invariance relates coefficients for fields and their charge conjugates on opposite orientations.

The result applies to general analytic 4D curved spacetimes, not just flat spacetime.

Abstract

We consider the operator product expansion for quantum field theories on general analytic 4-dimensional curved spacetimes within an axiomatic framework. We prove under certain general, model-independent assumptions that such an expansion necessarily has to be invariant under a simultaneous reversal of parity, time, and charge (PCT) in the following sense: The coefficients in the expansion of a product of fields on a curved spacetime with a given choice of time and space orientation are equal (modulo complex conjugation) to the coefficients for the product of the corresponding charge conjugate fields on the spacetime with the opposite time and space orientation. We propose that this result should be viewed as a replacement of the usual PCT theorem in Minkowski spacetime, at least in as far as the algebraic structure of the quantum fields at short distances is concerned.