Algebraic field theory on curved manifolds

Olesen, Martin

doi:10.1090/S0002-9947-1995-1189546-1

Algebraic field theory on curved manifolds
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by Martin Olesen

Trans. Amer. Math. Soc. 347 (1995), 2147-2160

DOI: https://doi.org/10.1090/S0002-9947-1995-1189546-1

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Abstract:

In this paper we set up an algebraic framework for the study of quantum field theory in a class of manifolds, which includes Minkowski space and the Kruskal spacetime. The formalism provides a unifying framework for studying problems of Bisognano-Wichmann type, e.g., Hawking radiation in black hole geometries. Analogously to flat spacetime, we establish a correspondence between isometries of certain wedge domains of spacetime and the modular structure of the local algebras. Under an ergodic hypothesis, the wedge algebras are shown to be type III factors as expected, and we derive a result concerning factorization of the equilibrium state. This result generalizes a similar one obtained by Sewell in [Ann. Phys. 141 (1982), 201-224]. Finally an example of a quantum field theory satisfying the basic axioms is constructed. The local algebras are field algebras of bosonic free field solutions to the Klein-Gordon equation twisted through a PCT-like conjugation, and we show that this model realizes the abstract properties developed on the axiomatic basis.

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