Hamiltonian and physical Hilbert space in polymer quantum mechanics

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dc.creatorCorichi, Alejandro
dc.creatorVukasinac, Tatjana
dc.creatorZapata, Jose A.
dc.date2006-10-16
dc.date2007-02-07
dc.date.accessioned2026-07-07T10:41:05Z
dc.date.available2026-07-07T10:41:05Z
dc.descriptionIn this paper, a version of polymer quantum mechanics, which is inspired by loop quantum gravity, is considered and shown to be equivalent, in a precise sense, to the standard, experimentally tested, Schroedinger quantum mechanics. The kinematical cornerstone of our framework is the so called polymer representation of the Heisenberg-Weyl (H-W) algebra, which is the starting point of the construction. The dynamics is constructed as a continuum limit of effective theories characterized by a scale, and requires a renormalization of the inner product. The result is a physical Hilbert space in which the continuum Hamiltonian can be represented and that is unitarily equivalent to the Schroedinger representation of quantum mechanics. As a concrete implementation of our formalism, the simple harmonic oscillator is fully developed.
dc.description19 pages, 2 figures. Comments and references added. Version to be published in CQG
dc.identifierhttps://arxiv.org/abs/gr-qc/0610072
dc.identifierhttp://arxiv.org/abs/gr-qc/0610072
dc.identifierClass.Quant.Grav.24:1495-1512,2007
dc.identifierdoi:10.1088/0264-9381/24/6/008
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/181520
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Physics
dc.titleHamiltonian and physical Hilbert space in polymer quantum mechanics
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