Adelic Quantum Mechanics: Nonarchimedean and Noncommutative Aspects

TL;DR

This paper reviews adelic quantum mechanics, highlighting its non-Archimedean and noncommutative features, including p-adic path integrals, quantum cosmology, and the p-adic Moyal product, drawing connections with q-analysis.

Contribution

It introduces the p-adic Moyal product and discusses the non-Archimedean and noncommutative aspects of adelic quantum mechanics, linking it with q-analysis.

Findings

Identification of similarities between p-adic analysis and q-analysis

Introduction of the p-adic Moyal product

Discussion of p-adic path integral and adelic quantum cosmology

Abstract

We present a short review of adelic quantum mechanics pointing out its non-Archimedean and noncommutative aspects. In particular, $p$-adic path integral and adelic quantum cosmology are considered. Some similarities between $p$-adic analysis and q-analysis are noted. The $p$-adic Moyal product is introduced.