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arXiv · 1401.7563

Optimal space of linear classical observables for Maxwell $k$-forms via spacelike and timelike compact de Rham cohomologies

Marco Benini
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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 Poincaré 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 Poincaré duality for the new cohomology groups.

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Marco Benini. 2014-01-29. Optimal space of linear classical observables for Maxwell $k$-forms via spacelike and timelike compact de Rham cohomologies. https://arxiv.org/abs/1401.7563

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