The operator product expansion for perturbative quantum field theory in curved spacetime

Abstract

We present an algorithm for constructing the Wilson operator product expansion (OPE) for perturbative interacting quantum field theory in general Lorentzian curved spacetimes, to arbitrary orders in perturbation theory. The remainder in this expansion is shown to go to zero at short distances in the sense of expectation values in arbitrary Hadamard states. We also establish a number of general properties of the OPE coefficients: (a) they only depend (locally and covariantly) upon the spacetime metric and coupling constants, (b) they satisfy an associativity property, (c) they satisfy a renormalization group equation, (d) they satisfy a certain microlocal wave front set condition, (e) they possess a ``scaling expansion''. The latter means that each OPE coefficient can be written as a sum of terms, each of which is the product of a curvature polynomial at a spacetime point, times a Lorentz invariant Minkowski distribution in the tangent space of that point. The algorithm is illustrated in an example.

45 pages, Latex, 4 figures

References in corpus (1)

• Phase space properties and the short distance structure in quantum field theory

Cited by in corpus (8)

• Emergent Gravity as the Eraser of Anomalous Gauge Boson Masses, and QFT-GR Concord
• An embedding formalism for CFTs in general states on curved backgrounds
• Quantum Inequalities from Operator Product Expansions
• Quantum field theory in curved spacetime, the operator product expansion, and dark energy
• Scaling algebras and pointlike fields: A nonperturbative approach to renormalization
• Quantum field theory in terms of consistency conditions I: General framework, and perturbation theory via Hochschild cohomology
• The Operator Product Expansion in Quantum Field Theory
• Locality in Abelian gauge theories over globally hyperbolic spacetimes