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arXiv · hep-th/0605156

Equations of motion, Noncommutativity and Quantization

Ignacio Cortese·J. Antonio García
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Abstract

We study the relation between a given set of equations of motion in configuration space and a Poisson bracket. A Poisson structure is consistent with the equations of motion if the symplectic form satisfy some consistency conditions. When the symplectic structure is commutative these conditions are the Helmholtz integrability equations for the nonrestricted inverse problem of the calculus of variations. We have found the corresponding consistency conditions for the symplectic noncommutative case.

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Ignacio Cortese, J. Antonio García. 2006-05-16. Equations of motion, Noncommutativity and Quantization. https://doi.org/10.1016/j.physleta.2006.05.044

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