Hadamard states for quantum Abelian duality

Abstract

Abelian duality is realized naturally by combining differential cohomology and locally covariant quantum field theory. This leads to a C${}^{\ast }$-algebra of observables, which encompasses the simultaneous discretization of both magnetic and electric fluxes. We discuss the assignment of physically well-behaved states to such algebra and the properties of the associated GNS triple. We show that the algebra of observables factorizes as a suitable tensor product of three C${}^{\ast }$-algebras: the first factor encodes dynamical information, while the other two capture topological data corresponding to electric and magnetic fluxes. On the former factor we exhibit a state whose two-point correlation function has the same singular structure of a Hadamard state. Specifying suitable counterparts also on the topological factors we obtain a state for the full theory, providing ultimately a unitary implementation of Abelian duality.

33 pages

References in corpus (7)

• The Uncertainty of Fluxes
• Heisenberg Groups and Noncommutative Fluxes
• Algebraic QFT in Curved Spacetime and quasifree Hadamard states: an introduction
• Electromagnetic duality anomaly in curved spacetimes
• Abelian duality on globally hyperbolic spacetimes
• Cheeger-Simons differential characters with compact support and Pontryagin duality
• Algebra of Observables and States for Quantum Abelian Duality

Cited by in corpus (2)

• Intertwining operators for symmetric hyperbolic systems on globally hyperbolic manifolds
• Homotopy theory of net representations