p-Adic and Adelic Quantum Mechanics
Abstract
Description
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.
18 pages, to be published in the Proceedings of the First Int. Conf. on p-Adic Mathematical Physics, 1-5 October 2003, Moscow
18 pages, to be published in the Proceedings of the First Int. Conf. on p-Adic Mathematical Physics, 1-5 October 2003, Moscow