## Abstract

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.

Original language | English |
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Pages (from-to) | 3325-3370 |

Number of pages | 46 |

Journal | Annales Henri Poincare |

Volume | 18 |

Issue number | 10 |

DOIs | |

Publication status | Published - Oct 2017 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Nuclear and High Energy Physics
- Mathematical Physics