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arXiv · 1412.4922

Incomplete Dirac reduction of constrained Hamiltonian systems

C. Chandre
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Abstract

First-class constraints constitute a potential obstacle to the computation of a Poisson bracket in Dirac's theory of constrained Hamiltonian systems. Using the pseudoinverse instead of the inverse of the matrix defined by the Poisson brackets between the constraints, we show that a Dirac-Poisson bracket can be constructed, even if it corresponds to an incomplete reduction of the original Hamiltonian system. The uniqueness of Dirac brackets is discussed.

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C. Chandre. 2014-12-16. Incomplete Dirac reduction of constrained Hamiltonian systems. https://arxiv.org/abs/1412.4922

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