A Dirac type xp-Model and the Riemann Zeros

TL;DR

This paper introduces a Dirac-type modification of the xp-model on a semi-infinite cylinder, aiming to realize the Berry-Keating conjecture and connect to physical systems like gapped graphene to study Riemann zeros.

Contribution

It presents a novel Dirac-type xp-model on a semi-infinite cylinder that supports the Berry-Keating conjecture and links to physical systems such as gapped graphene.

Findings

Realizes the Berry-Keating conjecture on Riemann zeros

Connects the model to gapped graphene with supercritical Coulomb charge

Provides a physical framework for studying Riemann zeros

Abstract

We propose a Dirac type modification of the xp-model to a $x \slashed{p}$ model on a semi-infinite cylinder. This model is inspired by recent work by Sierra et al on the xp-model on the half-line. Our model realizes the Berry-Keating conjecture on the Riemann zeros. We indicate the connection of our model to that of gapped graphene with a supercritical Coulomb charge, which might provide a physical system for the study of the zeros of the Riemann Zeta function.