Quantum Field Theory on Curved Backgrounds. II. Spacetime Symmetries

Details Quantum Field Theory on Curved Backgrounds. II. Spacetime Symmetries Quantum Field Theory on Curved Backgrounds. II. Spacetime Symmetries

2007-03-31

arxiv.org/abs/0704.0052v1

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, 1 figure

Scientific paper

We study space-time symmetries in scalar quantum field theory (including interacting theories) on static space-times. We first consider Euclidean quantum field theory on a static Riemannian manifold, and show that the isometry group is generated by one-parameter subgroups which have either self-adjoint or unitary quantizations. We analytically continue the self-adjoint semigroups to one-parameter unitary groups, and thus construct a unitary representation of the isometry group of the associated Lorentzian manifold. The method is illustrated for the example of hyperbolic space, whose Lorentzian continuation is Anti-de Sitter space.

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