p-Adic valued quantization

被引：38

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

共 38 条

[1]

Vladimirov V.S., Volovich I.V., Superanalysis. I. Differential calculus, Theor. Math. Phys., 59, pp. 317-335, (1984)

[2]

Vladimirov V.S., Volovich I.V., Superanalysis. II. Integral calculus, Theor. Math. Phys., 60, pp. 743-765, (1985)

[3]

Volovich I.V., p-Adic string, Class. Quant. Grav., 4, pp. 83-87, (1987)

[4]

Aref'eva I.Y., Dragovich B., Volovich I.V., On the p-adic summability of the anharmonic ocillator, Phys. Lett. B, 200, pp. 512-514, (1988)

[5]

Dragovich B., On signature change in p-adic space-time, Mod. Phys. Lett., 6, pp. 2301-2307, (1991)

[6]

Khrennikov A.Y., Mathematical methods of the non-archimedean physics, Uspekhi Mat. Nauk, 45, 4, pp. 79-110, (1990)

[7]

Khrennikov A.Y., Quantum mechanics over Galois extensions of number fields, Dokl. Akad. Nauk USSR, 315, pp. 860-864, (1990)

[8]

Khrennikov A.Y., p-Adic quantum mechanics with p-adic valued functions, J.Math. Phys., 32, pp. 932-937, (1991)

[9]

Khrennikov A.Y., Real-non-Archimedean structure of space-time, Theor. Math. Phys., 86, 2, pp. 177-190, (1991)

[10]

Khrennikov A.Y., p-Adic probability and statistics, Dokl. Akad. Nauk, 322, pp. 1075-1079, (1992)

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