Finite quantum models: constructive approach to description of quantum behavior

V. V. Kornyak

Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XIX, Tome 387 (2011), pp. 122-144

Résumé

Universality of quantum mechanics – its applicability to physical systems of quite different nature and scales – indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing indistinguishable, i.e. lying on the same orbit of some symmetry group, elements. In this paper we demonstrate, that quantum behavior arises naturally in systems with finite number of elements connected by nontrivial symmetry groups. The “finite” approach allows to see the peculiarities of quantum description more distinctly without need for concepts like “wave function collapse”, “Everett's multiverses” etc. In particular, under the finiteness assumption any quantum dynamics is reduced to the simple permutation dynamics. The advantage of the finite quantum models is that they can be studied constructively by means of computer algebra and computational group theory methods.