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}
}
  • V. Kornyak
  • Published 4 September 2017
  • Mathematics
  • arXiv: Quantum Physics
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… 
View PDF on arXiv
View With Semantic Reader
11 Citations
Background Citations
2
Methods Citations
1

Figures from this paper

11 Citations

Citation Type

Citation Type

Splitting Permutation Representations of Finite Groups by Polynomial Algebra Methods
TLDR
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
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
TLDR
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
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
  • V. Kornyak
  • Physics, Mathematics
    Discrete 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
  • V. Kornyak
  • Mathematics
    Journal of Physics: Conference Series
  • 2019
TLDR
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
  • V. Kornyak
  • Mathematics, Computer Science
    Journal of Mathematical Sciences
  • 2019
TLDR
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
  • V. Kornyak
  • Mathematics
    Journal 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
TLDR
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.
An Algorithm for Constructing Irreducible Decompositions of Permutation Representations of Wreath Products of Finite Groups
...
1
2
...

References

SHOWING 1-10 OF 15 REFERENCES
Combinatorial Approach to Modeling Quantum Systems
Using the fact that any linear representation of a group can be embedded into permutations, we propose a constructive description of quantum behavior that provides, in particular, a natural…
Discrete dynamical models: combinatorics, statistics and continuum approximations
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical…
Building up spacetime with quantum entanglement
In this essay, we argue that the emergence of classically connected spacetimes is intimately related to the quantum entanglement of degrees of freedom in a non-perturbative description of quantum…
Cool horizons for entangled black holes
General relativity contains solutions in which two distant black holes are connected through the interior via a wormhole, or Einstein‐Rosen bridge. These solutions can be interpreted as maximally…
Representation theory of finite groups and associated algebras
A loom sley capable of use in high speed looms comprises a substantially tubular member, said tubular member having attached thereto a race board plate and a reed support device, said race board…
Phys
  • Rev. D 95, 024031
  • 2017
EPJ Web of Conferences 108
  • 01007
  • 2016
Mathematical Modelling and Geometry
  • 3, No 1, 1–24
  • 2015
Classical and quantum discrete dynamical systems
We study deterministic and quantum dynamics from a constructive “finite” point of view, since the introduction of the continuum or other actual infinities in physics poses severe conceptual and…
Fortschr
  • Phys. 61 781–811
  • 2013
...
1
2
...