Annales Henri Poincaré

, Volume 18, Issue 10, pp 3325–3370 | Cite as

Hadamard States for Quantum Abelian Duality

  • Marco Benini
  • Matteo Capoferri
  • Claudio DappiaggiEmail author


Abelian duality is realized naturally by combining differential cohomology and locally covariant quantum field theory. This leads to a \(\hbox {C}^*\)-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 \(\hbox {C}^*\)-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.


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The authors are grateful to Nicolò Drago and Alexander Schenkel for stimulating discussions and valuable suggestions and would like to thank the anonymous referees for their encouragement towards improving the structure and clarity of the paper. M. C. and C. D. are grateful to the Institute of Mathematics of the University of Potsdam for the kind hospitality during the realization of part of this work. The work of M. B. has been supported by a research fellowship of the Alexander von Humboldt foundation. The work of M. C. has been partially supported by IUSS (Pavia). The work of C. D. has been supported by the University of Pavia.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Marco Benini
    • 1
  • Matteo Capoferri
    • 2
  • Claudio Dappiaggi
    • 3
    • 4
    Email author
  1. 1.Institut für MathematikUniversität PotsdamPotsdamGermany
  2. 2.Department of MathematicsUniversity College LondonLondonUK
  3. 3.Dipartimento di FisicaUniversità degli Studi di PaviaPaviaItaly
  4. 4.Istituto Nazionale di Fisica Nucleare - Sezione di PaviaPaviaItaly

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