Wavefront Sets in Algebraic Quantum Field Theory |
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Authors: | Rainer Verch |
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Institution: | Institut für Theoretische Physik, Universit?t G?ttingen, Bunsenstr. 9, D-37073 G?ttingen, Germany.?E-mail: verch@theorie.physik.uni-goettingen.de, DE
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Abstract: | The investigation of wavefront sets of n-point distributions in quantum field theory has recently acquired some attention stimulated by results obtained with the
help of concepts from microlocal analysis in quantum field theory in curved spacetime. In the present paper, the notion of
wavefront set of a distribution is generalized so as to be applicable to states and linear functionals on nets of operator
algebras carrying a covariant action of the translation group in arbitrary dimension. In the case where one is given a quantum
field theory in the operator algebraic framework, this generalized notion of wavefront set, called “asymptotic correlation
spectrum”, is further investigated and several of its properties for physical states are derived. We also investigate the
connection between the asymptotic correlation spectrum of a physical state and the wavefront sets of the corresponding Wightman
distributions if there is a Wightman field
affiliated to the local operator algebras. Finally we present a new result (generalizing known facts) which shows that certain
spacetime points must be contained in the singular supports of the 2n-point distributions of a non-trivial Wightman field.
Received: 27 July 1998 / Accepted: 3 March 1999 |
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