Polymer quantization versus the Snyder noncommutative space

Abstract

We study a noncanonical Hilbert space representation of the polymer quantum mechanics. It is shown that Heisenberg algebra get some modifications in the constructed setup from which a generalized uncertainty principle will naturally come out. Although the extracted physical results are the same as those obtained from the standard canonical representation, the noncanonical representation may be notable in view of its possible connection with the generalized uncertainty theories suggested by string theory. In this regard, by considering an Snyder-deformed Heisenberg algebra we show that since the translation group is not deformed it can be identified with a polymer-modified Heisenberg algebra. In classical level, it is shown the noncanonical Poisson brackets are related to their canonical counterparts by means of a Darboux transformation on the corresponding phase space.

14 pages, 1 figure, to appear in CQG

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Cited by in corpus (12)

• Recent progress on the description of relativistic spin: vector model of spinning particle and rotating body with gravimagnetic moment in General Relativity
• A new bound on polymer quantization via an opto-mechanical setup
• Generalized uncertainty principle or curved momentum space?
• Natural Cutoffs via Compact Symplectic Manifolds
• Bounds on quantum gravity parameter from the $SU(2)$ NJL effective model of QCD
• Classical polymerization of the Schwarzschild metric
• Semiclassical and Quantum Polymer Effects in the Flat Isotropic Universe
• Late time cosmic acceleration from natural infrared cutoff?
• Violation of the Holographic Principle in the Loop Quantum Gravity
• Black hole thermodynamics in Snyder phase space
• Photon gas thermodynamics in dS and AdS momentum spaces
• Superfluids in Polymer Quantum Mechanics