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arXiv · 2003.00388

The symplectic group in Polymer Quantum Mechanics

Angel Garcia-Chung
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Abstract

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 non-unitary evolution.

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BibTeXRIS

Angel Garcia-Chung. 2020-03-01. The symplectic group in Polymer Quantum Mechanics. https://doi.org/10.1103/physrevd.101.106004

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