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Regularized Algebraic Nets for General Covariant QFT on Differentiable Manifolds

M. Rainer
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Abstract

Quantum general relativity may be considered as generally covariant QFT on differentiable manifolds, without any a priori metric structure. The kinematically covariance group acts by general diffeomorphisms on the manifold and by automorphisms on the isotonic net of *-algebras encoding the QFT, while the algebra of observables is covariant under the dynamical subgroup of the general diffeomorphism group. Here, I focus on an algebraic implementation of the dynamical subgroup of dilations. Introducing an small and large scale cutoffs algebraically, their usual a priori conflict with general covariance is avoided. Thereby, a commutant duality between the minimal and maximal algebra is proposed. This allows to extract the modular structure, which is again related to the dilations.

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M. Rainer. 1997-05-30. Regularized Algebraic Nets for General Covariant QFT on Differentiable Manifolds. https://arxiv.org/abs/gr-qc/9705084

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