Abelian duality on globally hyperbolic spacetimes

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 $C^{\ast }$-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.

30 pages, no figures - Final version published in Communications in Mathematical Physics

References in corpus (2)

• The Uncertainty of Fluxes
• Heisenberg Groups and Noncommutative Fluxes

Cited by in corpus (9)

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• Higher Structures in Algebraic Quantum Field Theory
• Quantum field theories on categories fibered in groupoids
• Flux Quantization
• Flux Quantization on 11-dimensional Superspace
• A new class of Fermionic Projectors: Møller operators and mass oscillation properties
• Flux Quantization on Phase Space
• Hadamard states for quantum Abelian duality
• Quantum Observables of Quantized Fluxes