Modified commutation relationships from the Berry-Keating program

Abstract

Current approaches to quantum gravity suggest there should be a modification of the standard quantum mechanical commutator, $[\hat{x},\hat{p}]=i\hslash$. Typical modifications are phenomenological and designed to result in a minimal length scale. As a motivating principle for the modification of the position and momentum commutator, we assume the validity of a version of the Bender-Brody-Müller variant of the Berry-Keating approach to the Riemann hypothesis. We arrive at a family of modified position and momentum operators, and their associated modified commutator, which lead to a minimal length scale. Additionally, this larger family generalizes the Bender-Brody-Müller approach to the Riemann hypothesis.

14 pages, 0 figures revtex4. Version published in PRD

References in corpus (2)

• Universality of Quantum Gravity Corrections
• Discreteness of Space from the Generalized Uncertainty Principle

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