Abelian duality is realized naturally by combining differential cohomology and locally covariant quantum field theory. This leads to a C ∗-algebra of observables, which encompasses the simultaneous discretization of both magnetic and electric fluxes. We discuss the assignment of physically well-behaved states on this 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 ∗-algebras: the first factor encodes dynamical information, while the other two capture topological data corresponding to electric and magnetic fluxes. On the former factor and in the case of ultra-static globally hyperbolic spacetimes with compact Cauchy surfaces, 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, ultimately implementing Abelian duality transformations as Hilbert space isomorphisms.
CITATION STYLE
Benini, M., Capoferri, M., & Dappiaggi, C. (2017). Hadamard States for Quantum Abelian Duality. Annales Henri Poincare, 18(10), 3325–3370. https://doi.org/10.1007/s00023-017-0593-y
Mendeley helps you to discover research relevant for your work.