Modeling Quantum Behavior in the Framework of Permutation Groups

TL;DR

This paper proposes a finite group-based framework for quantum mechanics, replacing unitary groups with permutation group representations, and demonstrates its potential through computational methods and simulations.

Contribution

It introduces a novel approach to quantum modeling using permutation groups, bridging group theory with quantum concepts and computational techniques.

Findings

Permutation group representations can model quantum systems.

The approach clarifies physical concepts in quantum mechanics.

Computational methods validate the model's effectiveness.

Abstract

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.