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Dirac brackets from magnetic backgrounds

AuthorsIsidro, José M.
KeywordsDirac brackets
Generalized complex geometry
[MSC] Geometry and quantization, symplectic methods
[MSC] Applications to physics
Issue DateJun-2007
PublisherWorld Scientific Publishing
CitationInternational Journal of Geometric Methods in Modern Physics 4(4): 523-532 (2007)
AbstractIn symplectic mechanics, the magnetic term describing the interaction between a charged particle and an external magnetic field has to be introduced by hand. On the contrary, in generalized complex geometry, such magnetic terms in the symplectic form arise naturally by means of B-transformations. Here we prove that, regarding classical phase space as a generalized complex manifold, the transformation law for the symplectic form under the action of a weak magnetic field gives rise to Dirac's prescription for Poisson brackets in the presence of constraints.
Description10 pages.-- MSC codes: 81S10, 53Z05.-- ISI Article Identifier: 000251316400002.-- ArXiv pre-print available at: http://arxiv.org/abs/hep-th/0611026
Publisher version (URL)http://dx.doi.org/10.1142/S0219887807002181
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