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 explanation of the appearance of complex
numbers and unitarity in the formalism of quantum mechanics. In our approach,
the quantum behavior can be explained by the fundamental impossibility to trace
the identity of indistinguishable objects in their evolution. Any observation
only provides information about the invariant relations between such objects.
The trajectory of a quantum system is a sequence of unitary evolutions
interspersed with observations -- non-unitary projections. We suggest a scheme
to construct combinatorial models of quantum evolution. The principle of
selection of the most likely trajectories in such models via the large numbers
approximation leads in the continuum limit to the principle of least action
with the appropriate Lagrangians and deterministic evolution equations.Comment: 12 pages (12+ for version 2), based on plenary lecture at
Mathematical Modeling and Computational Physics 2015, Stara Lesna, High Tatra
Mountains, Slovakia, Jully 13--17, 201
