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A C ? -algebra for quantized principal U(1)-connections on globally hyperbolic lorentzian manifolds

Benini, Marco; Dappiaggi, Claudio; Hack, Thomas Paul; Schenkel, Alexander

Authors

Marco Benini

Claudio Dappiaggi

Thomas Paul Hack



Abstract

© Springer-Verlag Berlin Heidelberg 2014. The aim of this work is to complete our program on the quantization of connections on arbitrary principal U(1)-bundles over globally hyperbolic Lorentzian manifolds. In particular, we show that one can assign via a covariant functor to any such bundle an algebra of observables which separates gauge equivalence classes of connections. The C ∗ -algebra we construct generalizes the usual CCR-algebras, since, contrary to the standard field-theoretic models, it is based on a presymplectic Abelian group instead of a symplectic vector space. We prove a no-go theorem according to which neither this functor, nor any of its quotients, satisfies the strict axioms of general local covariance. As a byproduct, we prove that a morphism violates the locality axiom if and only if a certain induced morphism of cohomology groups is non-injective. We show then that, fixing any principal U(1)-bundle, there exists a suitable category of sub-bundles for which a quotient of our functor yields a quantum field theory in the sense of Haag and Kastler. We shall provide a physical interpretation of this feature and we obtain some new insights concerning electric charges in locally covariant quantum field theory.

Citation

Benini, M., Dappiaggi, C., Hack, T. P., & Schenkel, A. (2014). A C ? -algebra for quantized principal U(1)-connections on globally hyperbolic lorentzian manifolds. Communications in Mathematical Physics, 332(1), 477-504. https://doi.org/10.1007/s00220-014-2100-3

Journal Article Type Article
Acceptance Date Mar 20, 2014
Online Publication Date Jul 5, 2014
Publication Date Nov 30, 2014
Deposit Date Aug 22, 2019
Publicly Available Date Mar 29, 2024
Journal Communications in Mathematical Physics
Print ISSN 0010-3616
Electronic ISSN 1432-0916
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 332
Issue 1
Pages 477-504
DOI https://doi.org/10.1007/s00220-014-2100-3
Keywords Mathematical Physics; Statistical and Nonlinear Physics
Public URL https://nottingham-repository.worktribe.com/output/2460547
Publisher URL https://link.springer.com/article/10.1007%2Fs00220-014-2100-3

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