The symplectic group in Polymer Quantum Mechanics

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.

arXiv comment20 pages

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• The relation between the symplectic group $Sp(4,\mathbb{R})$ and its Lie algebra: its application in polymer quantum mechanics
• On the covariance matrix for Gaussian states
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