Incomplete Dirac reduction of constrained Hamiltonian systems

2014/12/16 by Chandre, C. · 2 citations
#Chaotic Dynamics (nlin.CD) #FOS: Physical sciences

paper · doi:10.48550/arxiv.1412.4922

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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• Imposing quasineutrality on electrostatic plasmas via the Dirac theory of constraints
• Poisson-Dirac Submanifolds as a Paradigm for Imposing Constraints in Non-dissipative Plasma Models

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