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Title: Incomplete Dirac reduction of constrained Hamiltonian systems

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.

Authors:
Publication Date:
OSTI Identifier:
22451228
Resource Type:
Journal Article
Journal Name:
Annals of Physics
Additional Journal Information:
Journal Volume: 361; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CALCULATION METHODS; DIRAC OPERATORS; HAMILTONIANS; MATRICES

Citation Formats

Chandre, C., E-mail: chandre@cpt.univ-mrs.fr. Incomplete Dirac reduction of constrained Hamiltonian systems. United States: N. p., 2015. Web. doi:10.1016/J.AOP.2015.06.011.
Chandre, C., E-mail: chandre@cpt.univ-mrs.fr. Incomplete Dirac reduction of constrained Hamiltonian systems. United States. https://doi.org/10.1016/J.AOP.2015.06.011
Chandre, C., E-mail: chandre@cpt.univ-mrs.fr. 2015. "Incomplete Dirac reduction of constrained Hamiltonian systems". United States. https://doi.org/10.1016/J.AOP.2015.06.011.
@article{osti_22451228,
title = {Incomplete Dirac reduction of constrained Hamiltonian systems},
author = {Chandre, C., E-mail: chandre@cpt.univ-mrs.fr},
abstractNote = {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.},
doi = {10.1016/J.AOP.2015.06.011},
url = {https://www.osti.gov/biblio/22451228}, journal = {Annals of Physics},
issn = {0003-4916},
number = ,
volume = 361,
place = {United States},
year = {Thu Oct 15 00:00:00 EDT 2015},
month = {Thu Oct 15 00:00:00 EDT 2015}
}