Abelian duality on globally hyperbolic spacetimes

Becker, Christian; Benini, Marco; Schenkel, Alexander; Szabo, Richard J.

Abstract

We study generalized electric/magnetic duality in Abelian gauge theory by combining techniques from locally covariant quantum field theory and Cheeger-Simons differential cohomology on the category of globally hyperbolic Lorentzian manifolds. Our approach generalizes previous treatments using the Hamiltonian formalism in a manifestly covariant way and without the assumption of compact Cauchy surfaces. We construct semi-classical configuration spaces and corresponding presymplectic Abelian groups of observables, which are quantized by the CCR-functor to the category of C*-algebras. We demonstrate explicitly how duality is implemented as a natural isomorphism between quantum field theories. We apply this formalism to develop a fully covariant quantum theory of self-dual fields.

Citation

Becker, C., Benini, M., Schenkel, A., & Szabo, R. J. (2017). Abelian duality on globally hyperbolic spacetimes. Communications in Mathematical Physics, 349(1), 361-392. https://doi.org/10.1007/s00220-016-2669-9

• Journal Article Type: Article
• Acceptance Date: Mar 18, 2016
• Online Publication Date: May 25, 2016
• Publication Date: Jan 31, 2017
• Deposit Date: Mar 2, 2017
• Publicly Available Date: Mar 2, 2017
• Journal: Communications in Mathematical Physics
• Print ISSN: 0010-3616
• Electronic ISSN: 1432-0916
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 349
• Issue: 1
• Pages: 361-392
• DOI: https://doi.org/10.1007/s00220-016-2669-9
• Keywords: Abelian gauge theory, Differential cohomology, Dirac charge quantization, Abelian duality, Self-dual Abelian gauge fields, Algebraic quantum field theory
• Public URL: https://nottingham-repository.worktribe.com/output/838127
• Publisher URL: https://doi.org/10.1007/s00220-016-2669-9
• Related Public URLs: https://arxiv.org/abs/1511.00316
• Additional Information: The final publication is available at Springer via https://doi.org/10.1007/s00220-016-2669-9