Reduced phase space: quotienting procedure for gauge theories

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dc.creatorPons, J M
dc.creatorSalisbury, D C
dc.creatorShepley, L C
dc.date1998-11-29
dc.date.accessioned2026-07-07T10:54:14Z
dc.date.available2026-07-07T10:54:14Z
dc.descriptionWe present a reduction procedure for gauge theories based on quotienting out the kernel of the presymplectic form in configuration-velocity space. Local expressions for a basis of this kernel are obtained using phase space procedures; the obstructions to the formulation of the dynamics in the reduced phase space are identified and circumvented. We show that this reduction procedure is equivalent to the standard Dirac method as long as the Dirac conjecture holds: that the Dirac Hamiltonian, containing the primary first class constraints, with their Lagrange multipliers, can be enlarged to an extended Dirac Hamiltonian which includes all first class constraints without any change of the dynamics. The quotienting procedure is always equivalent to the extended Dirac theory, even when it differs from the standard Dirac theory. The differences occur when there are ineffective constraints, and in these situations we conclude that the standard Dirac method is preferable --- at least for classical theories. An example is given to illustrate these features, as well as the possibility of having phase space formulations with an odd number of physical degrees of freedom.
dc.description14 pages; LaTeX2e; uses Institute of Physics packages To appear in J. Phys. A: Math. Gen. Vol 32 (1999)
dc.identifierhttps://arxiv.org/abs/math-ph/9811029
dc.identifierhttp://arxiv.org/abs/math-ph/9811029
dc.identifierJ.Phys.A32:419-430,1999
dc.identifierdoi:10.1088/0305-4470/32/2/015
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/185740
dc.subjectMathematical Physics
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Theory
dc.titleReduced phase space: quotienting procedure for gauge theories
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