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.Comment: 8 pages, based on plenary lecture at Mathematical Modeling and
Computational Physics 2017, Dubna, July 3--7, 201
