Quantum models based on finite groups
arXiv:1803.00408 · doi:10.1088/1742-6596/965/1/012023
Abstract
We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical content. Since any linear representation of a finite group can be implemented as a subrepresentation of a permutation representation, quantum-mechanical problems can be formulated in terms of permutation groups. Reproducing quantum behavior in the framework of permutation representations of finite groups makes it possible to clarify the meaning of a number of physical concepts.
12 pages, based on talk at ISQS-25, Prague, June 6-10, 2017. arXiv admin note: substantial text overlap with arXiv:1709.01831