Dynamical locality of the free Maxwell field

Chris Fewster, Benjamin Lang

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We consider the non-interacting source-free Maxwell field, described both in terms of the vector potential and the field strength. Starting from the classical field theory on contractible globally hyperbolic spacetimes, we extend the classical field theory to general globally hyperbolic spacetimes in two ways to obtain a "universal" theory and a "reduced" theory. The quantum field theory in terms of the unital $*$-algebra of the smeared quantum field is then obtained by an application of a suitable quantisation functor. We show that the universal theories fail local covariance and dynamical locality owing to the possibility of having non-trivial radicals in the classical and non-trivial centres in the quantum case. The reduced theories are both locally covariant and dynamically local. These models provide new examples relevant to the discussion of how theories should be formulated so as to describe the same physics in all spacetimes.
Original languageEnglish
Pages (from-to)401-436
JournalAnnales Henri Poincare
Issue number2
Early online date6 Mar 2015
Publication statusPublished - Feb 2016

Bibliographical note

27pp v3: Some comments added; minor corrections and typos fixed. © 2015 Springer Basel. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details


  • math-ph
  • math.MP

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