Equations of motion, Noncommutativity and Quantization
High Energy Physics - Theory
2008-11-26 v1 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
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.
Cite
@article{arxiv.hep-th/0605156,
title = {Equations of motion, Noncommutativity and Quantization},
author = {Ignacio Cortese and J. Antonio García},
journal= {arXiv preprint arXiv:hep-th/0605156},
year = {2008}
}
Comments
18 pages, to appear PLA