Dirac-like approach for consistent discretizations of classical constrained theories

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dc.creatorDi Bartolo, Cayetano
dc.creatorGambini, Rodolfo
dc.creatorPorto, Rafael
dc.creatorPullin, Jorge
dc.date2004-05-26
dc.date.accessioned2026-07-07T03:28:44Z
dc.date.available2026-07-07T03:28:44Z
dc.descriptionWe analyze the canonical treatment of classical constrained mechanical systems formulated with a discrete time. We prove that under very general conditions, it is possible to introduce nonsingular canonical transformations that preserve the constraint surface and the Poisson or Dirac bracket structure. The conditions for the preservation of the constraints are more stringent than in the continuous case and as a consequence some of the continuum constraints become second class upon discretization and need to be solved by fixing their associated Lagrange multipliers. The gauge invariance of the discrete theory is encoded in a set of arbitrary functions that appear in the generating function of the evolution equations. The resulting scheme is general enough to accommodate the treatment of field theories on the lattice. This paper attempts to clarify and put on sounder footing a discretization technique that has already been used to treat a variety of systems, including Yang--Mills theories, BF-theory and general relativity on the lattice.
dc.description11 pages, RevTeX
dc.identifierhttps://arxiv.org/abs/gr-qc/0405131
dc.identifierhttp://arxiv.org/abs/gr-qc/0405131
dc.identifierJ.Math.Phys. 46 (2005) 012901
dc.identifierdoi:10.1063/1.1823030
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/34943
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Lattice
dc.subjectHigh Energy Physics - Theory
dc.subjectClassical Physics
dc.titleDirac-like approach for consistent discretizations of classical constrained theories
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