Adelic Quantum Mechanics: Nonarchimedean and Noncommutative Aspects

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.

14 pages, Talk presented at the Conference: Noncommutative structures in mathematics and physics, Kiev, Sept. 24-27. 2000