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arXiv · 1810.03976

Modified commutation relationships from the Berry-Keating program

Michael Bishop·Erick Aiken·Douglas Singleton
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Abstract

Current approaches to quantum gravity suggest there should be a modification of the standard quantum mechanical commutator, $[{\hat x} , {\hat p}] = i \hbar$. 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-M\"uller 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-M\"uller approach to the Riemann hypothesis.

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Michael Bishop, Erick Aiken, Douglas Singleton. 2018-09-30. Modified commutation relationships from the Berry-Keating program. https://doi.org/10.1103/physrevd.99.026012

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