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Algebraic Quantum Theory on Manifolds: A Haag-Kastler Setting for Quantum Geometry

Martin Rainer
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Abstract

Motivated by the invariance of current representations of quantum gravity under diffeomorphisms much more general than isometries, the Haag-Kastler setting is extended to manifolds without metric background structure. First, the causal structure on a differentiable manifold M of arbitrary dimension (d+1>2) can be defined in purely topological terms, via cones (C-causality). Then, the general structure of a net of C*-algebras on a manifold M and its causal properties required for an algebraic quantum field theory can be described as an extension of the Haag-Kastler axiomatic framework. An important application is given with quantum geometry on a spatial slice within the causally exterior region of a topological horizon H, resulting in a net of Weyl algebras for states with an infinite number of intersection points of edges and transversal (d-1)-faces within any neighbourhood of the spatial boundary S^2.

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Martin Rainer. 2000-03-14. Algebraic Quantum Theory on Manifolds: A Haag-Kastler Setting for Quantum Geometry. https://doi.org/10.1088/0264-9381%2F17%2F9%2F305

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