p-Adic valued quantization

被引：37

作者：

Albeverio S. ^{[1
]}

Cianci R. ^{[2
]}

Khrennikov A.Y. ^{[3
]}

机构：

[1] Chair of Stochastic Analysis, Institute of Applied Mathematics, Bonn University, Bonn

[2] DIPTEM, University of Genova, Genova

[3] Center for Mathematical Modeling in Physics and Cognitive Sciences, Växjö University, Växjö

来源：

P-Adic Numbers, Ultrametric Analysis, and Applications | 2009年 / 1卷 / 2期

关键词：

bounded operators; p-adic quantization; p-adic valued wave function; position and momentum operators;

D O I：

10.1134/S2070046609020010

中图分类号：

学科分类号：

摘要：

This review covers an important domain of p-adic mathematical physics — quantum mechanics with p-adic valued wave functions. We start with basic mathematical constructions of this quantum model: Hilbert spaces over quadratic extensions of the field of p-adic numbers ℚp, operators — symmetric, unitary, isometric, one-parameter groups of unitary isometric operators, the p-adic version of Schrödinger’s quantization, representation of canonical commutation relations in Heisenberg andWeyl forms, spectral properties of the operator of p-adic coordinate.We also present postulates of p-adic valued quantization. Here observables as well as probabilities take values in ℚp. A physical interpretation of p-adic quantities is provided through approximation by rational numbers. © 2009, Pleiades Publishing, Ltd.

引用

页码：91 / 104

页数：13

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