Abstract
The extent to which the non-interacting and source-free Maxwell field obeys the condition of dynamical locality is determined in various formulations. Starting from contractible globally hyperbolic spacetimes, we extend the classical field theory to globally hyperbolic spacetimes of arbitrary topology in two ways, obtaining a ‘universal’ theory and a ‘reduced’ theory of the classical free Maxwell field and their corresponding quantisations. We show that the classical and the quantised universal theory fail local covariance and dynamical locality owing to the possibility of having non-trivial radicals in the classical pre-symplectic spaces and non-trivial centres in the quantised *-algebras. The classical and the quantised reduced theory are both locally covariant and dynamically local, thus closing a gap in the discussion of dynamical locality and providing new examples relevant to the question of how theories should be formulated so as to describe the same physics in all spacetimes.
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Communicated by Karl-Henning Rehren
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Fewster, C.J., Lang, B. Dynamical Locality of the Free Maxwell Field. Ann. Henri Poincaré 17, 401–436 (2016). https://doi.org/10.1007/s00023-015-0398-9
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DOI: https://doi.org/10.1007/s00023-015-0398-9