# Modeling Quantum Behavior in the Framework of Permutation Groups

@article{Kornyak2017ModelingQB, title={Modeling Quantum Behavior in the Framework of Permutation Groups}, author={Vladimir V. Kornyak}, journal={arXiv: Quantum Physics}, year={2017} }

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…

## 11 Citations

Splitting Permutation Representations of Finite Groups by Polynomial Algebra Methods

- Mathematics, Computer ScienceCASC
- 2018

An algorithm for splitting permutation representations of a finite group over fields of characteristic zero into irreducible components is described, which is an important part of the solution of systems of quadratic equations.

Computation of Irreducible Decompositions of Permutation Representations of Wreath Products of Finite Groups

- Mathematics
- 2020

Abstract An algorithm for the computation of the complete set of primitive orthogonal idempotents of the centralizer ring of the permutation representation of the wreath product of finite groups is…

An Algorithm to Decompose Permutation Representations of Finite Groups: Polynomial Algebra Approach

- Mathematics, Computer ScienceArXiv
- 2018

An algorithm for splitting a permutation representation of a finite group into irreducible components is described, based on the fact that the components of the invariant inner product in invariant subspaces are operators of projection into these subspaced.

Multipartite Quantum Systems and Representations of Wreath Products

- MathematicsEPJ Web of Conferences
- 2020

The multipartite quantum systems are of particular interest for the study of such phenomena as entanglement and non-local correlations. The symmetry group of the whole multipartite system is the…

Quantum mereology in finite quantum mechanics

- Physics, MathematicsDiscrete and Continuous Models and Applied Computational Science
- 2021

Any Hilbert space with composite dimension can be factored into a tensor product of smaller Hilbert spaces. This allows us to decompose a quantum system into subsystems. We propose a model based on…

A new algorithm for irreducible decomposition of representations of finite groups

- MathematicsJournal of Physics: Conference Series
- 2019

An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero using the fact that the decomposition induces a partition of the invariant inner product into a complete set of mutually orthogonal projectors is described.

An Algorithm for Decomposing Representations of Finite Groups Using Invariant Projections

- Mathematics, Computer ScienceJournal of Mathematical Sciences
- 2019

An algorithm for decomposing permutation representations of finite groups over fields of characteristic zero into irreducible components is described, which allows us to reduce the problem to solving systems of quadratic equations.

Subsystems of a Closed Quantum System in Finite Quantum Mechanics

- MathematicsJournal of Mathematical Sciences
- 2022

Any Hilbert space of composite dimension can be decomposed into a tensor product of Hilbert spaces of lower dimensions. Such a factorization makes it possible to decompose a quantum system into…

Decomposition of a Quantum System Into Subsystems in Finite Quantum Mechanics

- Mathematics, PhysicsArXiv
- 2021

A simple tractable model for a constructive study of decompositions of quantum systems is proposed and it is shown that any Hilbert space with composite dimension can be factorized into a tensor product of smaller Hilbert spaces.

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