On a commutative ring structure in quantum mechanics

TL;DR

This paper introduces a new commutative ring structure in quantum mechanics inspired by multi-photon absorption, enabling an operator representation of the Riemann zeta function.

Contribution

It proposes the concept of the p-on, modeling multi-photon processes, and establishes a novel algebraic framework in quantum mechanics.

Findings

Defines the p-on as a new quantum operator

Provides an operator representation of the Riemann zeta function

Establishes a commutative ring structure in quantum mechanics

Abstract

In this article, I propose a concept of the $p$-on which is modelled on the multi-photon absorptions in quantum optics. It provides a commutative ring structure in quantum mechanics. Using it, I will give an operator representation of the Riemann $\zeta$ function.