The symplectic group in Polymer Quantum Mechanics
Abstract
In this paper we provide the representation of the symplectic group Sp(2n, 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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