p-Adic and Adelic Quantum Mechanics

TL;DR

This paper reviews p-adic and adelic quantum mechanics, exploring their formulations, applications in cosmology and string theory, and revealing how adelic effects induce spacetime discreteness depending on quantum states.

Contribution

It provides a comprehensive review of p-adic and adelic quantum mechanics and introduces new results on their implications for spacetime structure.

Findings

p-adic effects lead to spacetime discreteness

Adelic approach links quantum states to spacetime properties

New results on p-adic and adelic quantum phenomena

Abstract

p-Adic mathematical physics emerged as a result of efforts to find a non-Archimedean approach to the spacetime and string dynamics at the Planck scale. One of its main achievements is a successful formulation and development of p-adic and adelic quantum mechanics, which have complex-valued wave functions of p-adic and adelic arguments, respectively. Various aspects of these quantum mechanics are reviewed here. In particular, the corresponding Feynman's path integrals, some minisuperspace cosmological models, and relevant approache to string theory, are presented. As a result of adelic approach, p-adic effects exhibit a spacetime and some other discreteness, which depend on the adelic quantum state of the physical system under consideration. Besides review, this article contains also some new results.