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  Microlocal spectrum condition and Hadamard form for vector-valued quantum fields in curved spacetime

Sahlmann, H., & Verch, R. (2001). Microlocal spectrum condition and Hadamard form for vector-valued quantum fields in curved spacetime. Reviews in Mathematical Physics, 13, 1203-1246.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-5653-F Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-5654-D
Genre: Journal Article

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2701.pdf (Preprint), 463KB
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 Creators:
Sahlmann, Hanno1, Author
Verch, Rainer, Author
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1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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 Abstract: The characterization of Hadamard states in terms of a specific form of the wavefront set of their two-point functions has been developed some years ago by Radzikowski for scalar fields on a four-dimensional globally hyperbolic spacetime, and initiated a major progress in the understanding of Hadamard states and the further development of quantum field theory in curved spacetime. In the present work, the characterization of Hadamard states through a particular form of the wavefront set of their two-point functions will be generalized from scalar fields to vector fields (sections in a vector bundle) which are subject to a wave-equation and are quantized so as to fulfill the covariant canonical commutation relations, or which obey a Dirac equation and are quantized according to the covariant anti-commutation relations, in any globally hyperbolic spacetime having dimension three or higher. In proving this result, a gap which is present in the published proof for the scalar field case will be removed. Moreover we determine the short-distance scaling limits of Hadamard states for vector-bundle valued fields, finding them to coincide with the corresponding flat-space, massless vacuum states.

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Language(s): eng - English
 Dates: 2001
 Publication Status: Published in print
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Title: Reviews in Mathematical Physics
Source Genre: Journal
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Pages: - Volume / Issue: 13 Sequence Number: - Start / End Page: 1203 - 1246 Identifier: -