Computations in Finite Groups and Quantum Physics

  • Vladimir V. Kornyak
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6885)

Abstract

Mathematical core of quantum mechanics is the theory of unitary representations of symmetries of physical systems. We argue that quantum behavior is a natural result of extraction of “observable” information about systems containing “unobservable” elements in their descriptions. Since our aim is physics where the choice between finite and infinite descriptions can not have any empirical consequences, we consider the problem in the finite background. Besides, there are many indications from observations — from the lepton mixing data, for example — that finite groups underly phenomena in particle physics at the deep level. The “finite” approach allows to reduce any quantum dynamics to the simple permutation dynamics and, thus, to express quantum observables in terms of permutation invariants of symmetry groups and their integer characteristics such as sizes of conjugate classes, sizes of group orbits, class coefficients, and dimensions of representations. Our study has been accompanied by computations with finite groups, their representations and invariants. We have used both our C implementation of algorithms for working with groups and computer algebra system GAP.

Keywords

Irreducible Representation Finite Group Conjugacy Class Invariant Subspace Permutation Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Vladimir V. Kornyak
    • 1
  1. 1.Laboratory of Information TechnologiesJoint Institute for Nuclear ResearchDubnaRussia

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