Quantum Field Theory on Curved Backgrounds, I. The Euclidean Functional Integral

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dc.creatorJaffe, Arthur
dc.creatorRitter, Gordon
dc.date2006-08-31
dc.date.accessioned2026-07-07T11:07:12Z
dc.date.available2026-07-07T11:07:12Z
dc.descriptionWe give a mathematical construction of Euclidean quantum field theory on certain curved backgrounds. We focus on generalizing Osterwalder-Schrader quantization, as these methods have proved useful to establish estimates for interacting fields on flat space-times. In this picture, a static Killing vector generates translations in Euclidean time, and physical positivity is played by positivity under reflection of Euclidean time. We discuss the quantization of flows which correspond to classical space-time symmetries, and give a general set of conditions which imply that broad classes of operators in the classical picture give rise to well-defined operators on the quantum-field Hilbert space. In particular, Killing fields on spatial sections give rise to unitary groups on the quantum-field Hilbert space, and corresponding densely-defined self-adjoint generators. We construct the Schrödinger representation using a method which involves localizing certain integrals over the full manifold to integrals over a codimension-one submanifold. This method is called sharp-time localization, and implies reflection positivity.
dc.description33 pages
dc.identifierhttps://arxiv.org/abs/hep-th/0609003
dc.identifierhttp://arxiv.org/abs/hep-th/0609003
dc.identifierCommun.Math.Phys.270:545-572,2007
dc.identifierdoi:10.1007/s00220-006-0166-2
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/189764
dc.subjectHigh Energy Physics - Theory
dc.titleQuantum Field Theory on Curved Backgrounds, I. The Euclidean Functional Integral
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