Hadamard States for Quantum Abelian Duality
- Abelian duality is realized naturally by combining differential cohomology and locally covariant quantum field theory. This leads to a -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 -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.
Author details: | Marco BeniniORCiDGND, Matteo Capoferri, Claudio Dappiaggi |
---|---|
DOI: | https://doi.org/10.1007/s00023-017-0593-y |
ISSN: | 1424-0637 |
ISSN: | 1424-0661 |
Title of parent work (English): | Annales de l'Institut Henri Poincaré |
Publisher: | Springer |
Place of publishing: | Basel |
Publication type: | Article |
Language: | English |
Year of first publication: | 2017 |
Publication year: | 2017 |
Release date: | 2020/04/20 |
Volume: | 18 |
Number of pages: | 46 |
First page: | 3325 |
Last Page: | 3370 |
Funding institution: | Alexander von Humboldt foundation; IUSS (Pavia); University of Pavia |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer review: | Referiert |