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A Poisson Algebra for Abelian Yang-Mills Fields on Riemannian Manifolds with Boundary

Facultad de Ciencias Físico-Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Morelia C.P. 58060, Mexico
Current address: Ciudad Universitaria, Morelia C.P. 58060, Michoacán, México.
Symmetry 2019, 11(7), 880; https://doi.org/10.3390/sym11070880
Received: 28 May 2019 / Accepted: 4 June 2019 / Published: 4 July 2019
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PDF [357 KB, uploaded 4 July 2019]

Abstract

We define a family of observables for abelian Yang-Mills fields associated to compact regions U M with smooth boundary in Riemannian manifolds. Each observable is parametrized by a first variation of solutions and arises as the integration of gauge invariant conserved current along admissible hypersurfaces contained in the region. The Poisson bracket uses the integration of a canonical multisymplectic current. View Full-Text
Keywords: Yang-Mills gauge fields; variational bicomplex; riemannian manifold; conserved currents Yang-Mills gauge fields; variational bicomplex; riemannian manifold; conserved currents
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Díaz-Marín, H.G. A Poisson Algebra for Abelian Yang-Mills Fields on Riemannian Manifolds with Boundary. Symmetry 2019, 11, 880.

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