Axiomatic Quantum Field Theory in Curved Spacetime

By S. Hollands, R. Wald. 2008

168 citations recorded by the source corpus.

The usual formulations of quantum field theory in Minkowski spacetime make crucial use of features—such as Poincaré invariance and the existence of a preferred vacuum state—that are very special to Minkowski spacetime. In order to generalize the formulation of quantum field theory to arbitrary globally hyperbolic curved spacetimes, it is essential that the theory be formulated in an entirely local and covariant manner, without assuming the presence of a preferred state. We propose a new framework for quantum field theory, in which the existence of an Operator Product Expansion (OPE) is elevated to a fundamental status, and, in essence, all of the properties of the quantum field theory are determined by its OPE. We provide general axioms for the OPE coefficients of a quantum field theory. These include a local and covariance assumption (implying that the quantum field theory is constructed in a local and covariant manner from the spacetime metric and other background structure, such as time and space orientations), a microlocal spectrum condition, an “associativity” condition, and the requirement that the coefficient of the identity in the OPE of the product of a field with its adjoint have positive scaling degree. We prove curved spacetime versions of the spin-statistics theorem and the PCT theorem. Some potentially significant further implications of our new viewpoint on quantum field theory are discussed.

Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/445d3e710a914bd0114a209770646761bcf6b59b

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In Atomic and Molecular Physics, and Optics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Analyticity and the Unruh effect: a study of local modular flow (2024, background): “…i.e., we will assume that there is a dense subspace of H that is included in the domain of every product This assumption allows us to multiply field operators together, and follows naturally from basic axiomatic assumptions about quantum field theory in general backgrounds — see e.g. [45, page 3].”
On the architecture of spacetime geometry (2012, background): “For free fields, this is essentially the definition of Hadamard states, and for interacting fields, this Hadamard-like property can be seen as a defining characteristic of the relevant states [33].”
A general proof of the quantum null energy condition (2017, background): “It turns out that β is sensitive to the local extrinsic curvature of the defect at y = 0, in analogy to regular OPE coefficients being sensitive to local curvature invariance of the metric if we make an OPE expansion of two local CFT operators in curved space [75].”