A framework for nonrelativistic isotropic models based on generalized uncertainty principles

Abstract

The existence of a fundamental length scale in Nature is a common prediction of distinct quantum gravity models. Discovery of such would profoundly change current knowledge of quantum phenomena and modifications to the Heisenberg uncertainty principle may be expected. Despite the attention given to this possibility in the past decades, there has been no common framework for a systematic investigation of so called generalized uncertainty principles (GUP). In this work we provide such framework in the context of nonrelativistic quantum mechanics. Our approach is based on very few assumptions: there is a fundamental length scale, space isotropy, invariance under parity and time reversal transformations, and symmetricity of the position and momentum operators. We show simple dimensional analysis allows for building a unified framework containing any isotropic generalized uncertainty principle (iGUP) and discuss some popular GUP models in this context after elaborating on relevant theoretical aspects of the framework. At last, we translate current bounds on three often investigated GUP models into bounds on parameters of such unified iGUP framework.

Accepted version. Includes bounds on GUP parameters derived from the SME

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Cited by in corpus (7)

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• Black hole interior quantization: a minimal uncertainty approach
• Space and time transformations with a minimal length
• Dark Matter as an effect of a minimal length
• On the algebraic approach to GUP in anisotropic space
• Finite Temperature Considerations in the Structure of Quadratic GUP-modified White Dwarfs
• Remarks on the quasi-position representation in models of generalized uncertainty principle