We construct the quantum propagator of the free particle in the polymer representation of quantum mechanics, both in position and momentum polarization. We verify the propagator satisfies standard properties such as composition, and that it reduces to the usual Schrödinger propagator in the limit of small parameter μ0, the length scale introduced in the polymer dynamics.

AIP conference proceedingsJan 1, 20122 citations

Quantum Theory of Polymers

J. M. André, J. Delhalle, Janos J. Ladik

Springer eBooksJan 1, 197871 citations

arXiv:1302.1906 · Annals of Physics

Propagators in polymer quantum mechanics

Ernesto Flores-González, Hugo Aurelio Morales-Técotl, Juan D. Reyes

Published Jun 12, 2013• 36 citations

arXiv HTML PDF

DOI: 10.1016/j.aop.2013.05.005

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Free particle propagator in polymer quantum mechanics

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In this paper, we provide the representation of the symplectic group

Sp(2n,\mathbb{R})

in polymer quantum mechanics. We derive the propagator of the polymer free particle and the polymer harmonic oscillator without considering a polymer scale. The polymer scale is then introduced to reconcile our results with those expressions for the polymer free particle. The propagator for the polymer harmonic oscillator implies nonunitary evolution.