Combinatorial Approach to Modeling Quantum Systems

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 the quantum mechanics. In o...

Full description

Saved in:
Bibliographic Details
Published inEPJ Web of Conferences Vol. 108; p. 1007
Main Author Kornyak, Vladimir V.
Format Journal Article Conference Proceeding
LanguageEnglish
Published Les Ulis EDP Sciences 01.01.2016
Subjects
Combinatorial analysis
Complex numbers
Evolution
Permutations
Principle of least action
Quantum mechanics
Quantum theory
Trajectories
Online AccessGet full text

Cover

More Information
Summary: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 the quantum mechanics. In our approach, the quantum behavior can be explained by the fundamental impossibility to trace the identity of the 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
ISSN:2100-014X
2101-6275
2100-014X
DOI:10.1051/epjconf/201610801007