@article{Benini2016,
  author    = {Benini, Marco},
  title     = {Optimal space of linear classical observables for Maxwell k-forms via spacelike and timelike compact de Rham cohomologies},
  series = {Journal of mathematical physics},
  volume    = {57},
  journal   = {Journal of mathematical physics},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {0022-2488},
  doi       = {10.1063/1.4947563},
  pages     = {1249 -- 1279},
  year      = {2016},
  abstract  = {Being motivated by open questions in gauge field theories, we consider non-standard de Rham cohomology groups for timelike compact and spacelike compact support systems. These cohomology groups are shown to be isomorphic respectively to the usual de Rham cohomology of a spacelike Cauchy surface and its counterpart with compact support. Furthermore, an analog of the usual Poincare duality for de Rham cohomology is shown to hold for the case with non-standard supports as well. We apply these results to find optimal spaces of linear observables for analogs of arbitrary degree k of both the vector potential and the Faraday tensor. The term optimal has to be intended in the following sense: The spaces of linear observables we consider distinguish between different configurations; in addition to that, there are no redundant observables. This last point in particular heavily relies on the analog of Poincare duality for the new cohomology groups. Published by AIP Publishing.},
  language  = {en}
}