Optimal space of linear classical observables for Maxwell k-forms via spacelike and timelike compact de Rham cohomologies
- Dipartimento di Fisica, Università di Pavia and INFN, Sezione di Pavia—Via Bassi 6, I-27100 Pavia (Italy)
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.
- OSTI ID:
- 22597063
- Journal Information:
- Journal of Mathematical Physics, Vol. 57, Issue 5; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
Similar Records
de Rham cohomology of SO(n) by supersymmetric quantum mechanics
Comments on the quantum field theory of the Coulomb gas formalism