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arXiv · 1805.05943

Polymer Quantum Mechanics as a Deformation Quantization

Jasel Berra-Montiel·Alberto Molgado
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Abstract

We analyze the polymer representation of quantum mechanics within the deformation quantization formalism. In particular, we construct the Wigner function and the star-product for the polymer representation as a distributional limit of the Schrödinger representation for the Weyl algebra in a Gaussian weighted measure, and we observe that the quasi-probability distribution limit of this Schrödinger representation agrees with the Wigner function for Loop Quantum Cosmology. Further, the introduced polymer star-product fulfills Bohr's correspondence principle even though not all the operators are well defined in the polymer representation. Finally, within our framework, we also derive a generalized uncertainty principle which is consistent to the ones usually obtained in theories assuming a fundamental minimal length in their formulation.

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Jasel Berra-Montiel, Alberto Molgado. 2019-01-31. Polymer Quantum Mechanics as a Deformation Quantization. https://doi.org/10.1088/1361-6382%2Faaf4e3

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