The Operator Product Expansion in Quantum Field Theory

2023/12/02 by Hollands, Stefan, Wald, Robert M.
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2312.01096

Abstract

Operator product expansions (OPEs) in quantum field theory (QFT) provide an asymptotic relation between products of local fields defined at points x₁, …, x_n and local fields at point y in the limit x₁, …, x_n → y. They thereby capture in a precise way the singular behavior of products of quantum fields at a point as well as their ``finite trends.'' In this article, we shall review the fundamental properties of OPEs and their role in the formulation of interacting QFT in curved spacetime, the ``flow relations'' in coupling parameters satisfied by the OPE coefficients, the role of OPEs in conformal field theories, and the manner in which general theorems -- specifically, the PCT theorem -- can be formulated using OPEs in a curved spacetime setting.

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