Incomplete Dirac reduction of constrained Hamiltonian systems |
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Authors: | C Chandre |
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Institution: | Centre de Physique Théorique, CNRS–Aix-Marseille Université, Campus de Luminy, case 907, 13009 Marseille, France |
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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. The relevance of this procedure for infinite dimensional Hamiltonian systems is exemplified. |
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Keywords: | Constrained Hamiltonian systems Dirac brackets Poisson brackets Jacobi identity |
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