Optimal space of linear classical observables for Maxwell k-forms via spacelike and timelike compact de Rham cohomologies
- 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.
Author details: | Marco BeniniORCiDGND |
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DOI: | https://doi.org/10.1063/1.4947563 |
ISSN: | 0022-2488 |
ISSN: | 1089-7658 |
Title of parent work (English): | Journal of mathematical physics |
Publisher: | American Institute of Physics |
Place of publishing: | Melville |
Publication type: | Article |
Language: | English |
Year of first publication: | 2016 |
Publication year: | 2016 |
Release date: | 2020/03/22 |
Volume: | 57 |
Number of pages: | 21 |
First page: | 1249 |
Last Page: | 1279 |
Funding institution: | University of Pavia |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer review: | Referiert |