English

The symplectic group in Polymer Quantum Mechanics

General Relativity and Quantum Cosmology 2020-05-13 v1 Mathematical Physics math.MP Quantum Physics

Abstract

In this paper we provide the representation of the symplectic group Sp(2n,R)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.

Cite

@article{arxiv.2003.00388,
  title  = {The symplectic group in Polymer Quantum Mechanics},
  author = {Angel Garcia-Chung},
  journal= {arXiv preprint arXiv:2003.00388},
  year   = {2020}
}

Comments

20 pages

R2 v1 2026-06-23T13:59:04.969Z