Marco Benini
A C ? -algebra for quantized principal U(1)-connections on globally hyperbolic lorentzian manifolds
Benini, Marco; Dappiaggi, Claudio; Hack, Thomas Paul; Schenkel, Alexander
Authors
Claudio Dappiaggi
Thomas Paul Hack
ALEXANDER SCHENKEL ALEXANDER.SCHENKEL@NOTTINGHAM.AC.UK
Associate Professor
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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A C*-algebra for quantized principal U(1)-connections on globally hyperbolic Lorentzian manifolds
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