ФИЗИКА ЭЛЕМЕНТАРНЫХ ЧАСТИЦ И АТОМНОГО ЯДРА

Конструктивная квантовая механика, основанная на конечных группах

Vladimir V. Kornyak, В. В. Корняк

Published Sep 24, 2025• 0 citations

Abstract

A formulation of quantum mechanics based on replacing the general unitary group by finite groups is considered. To solve problems arising in the context of this formulation, we use computer algebra and computational group theory methods.

Related papers

Constructive Quantum Mechanics Based on Finite Groups

Vladimir V. Kornyak

Abstract A formulation of quantum mechanics based on replacing the general unitary group by finite groups is considered. To solve problems arising in the context of this formulation, we use computer algebra and computational group theory methods.

arXiv:2409.18159Physics of Particles and NucleiAug 1, 20250 citations

Constructive Quantum Mechanics and Calculations with Finite Groups

Vladimir V. Kornyak

Abstract Application of computer algebra and computational group theory to the study of problems arising in constructive quantum mechanics is considered.

Programming and Computer SoftwareFeb 1, 20250 citations

CONSTRUCTIVE QUANTUM MECHANICS AND CALCULATIONS WITH FINITE GROUPS

Vladimir V. Kornyak

Application of computer algebra and computational group theory to the study of problems arising in constructive quantum mechanics is considered.

Programming and Computer SoftwareJan 1, 20250 citations

Квантовая механика на одномерных геометриях Кэли-Клейна quantum mechanics on one-di- mentional Cayley-Klein geometries

Nikolay Gromov, Куратов Василий Васильевич

Jan 1, 20170 citations

Modeling Quantum Behavior in the Framework of Permutation Groups

Vladimir V. Kornyak

Quantum-mechanical concepts can be formulated in constructive finite terms without loss of their empirical content if we replace a general unitary group by a unitary representation of a finite group. Any linear representation of a finite group can be realized as a subrepresentation of a permutation representation. Thus, quantum-mechanical problems can be expressed in terms of permutation groups. This approach allows us to clarify the meaning of a number of physical concepts. Combining methods of computational group theory with Monte Carlo simulation we study a model based on representations of permutation groups.

arXiv:1709.01831EPJ Web of ConferencesJan 1, 201816 citations

Quantum Mechanics on Finite Groups

Stanley Gudder

Foundations of PhysicsMay 11, 20062 citations