# Hadamard states for quantum Abelian duality

November 30, 2016

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 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$^*$-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.

open access link
Ann. Henri PoincarĂ© 18(10), 3325-3370 (2017)

@article{Benini:2016riy,
author = "Benini, Marco and Capoferri, Matteo and Dappiaggi,
Claudio",
title = "{Hadamard states for quantum Abelian duality}",
journal = "Annales Henri Poincare",
volume = "18",
year = "2017",
number = "10",
pages = "3325-3370",
doi = "10.1007/s00023-017-0593-y",
eprint = "1611.10282",
archivePrefix = "arXiv",
primaryClass = "math-ph",
SLACcitation = "%%CITATION = ARXIV:1611.10282;%%"
}

Keywords:

Abelian duality, Abelian gauge theory, Hadamard states