Journal of Generalized Lie Theory and Applications

Hidden structures in quantum mechanics

Vladimir DZHUNUSHALIEV

Full-text: Open access

Abstract

It is shown that some operators in quantum mechanics have hidden structures that are unobservable in principle. These structures are based on a supersymmetric decomposition of the momentum operator, and a nonassociative decomposition of the spin operator.

Article information

Source
J. Gen. Lie Theory Appl., Volume 3, Number 1 (2009), Article ID S080102, 33-38.

Dates
First available in Project Euclid: 19 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.jglta/1319028473

Digital Object Identifier
doi:10.4303/jglta/S080102

Mathematical Reviews number (MathSciNet)
MR2486608

Zentralblatt MATH identifier
1162.81386

Subjects
Primary: 81R15: Operator algebra methods [See also 46Lxx, 81T05]

Citation

DZHUNUSHALIEV, Vladimir. Hidden structures in quantum mechanics. J. Gen. Lie Theory Appl. 3 (2009), no. 1, Article ID S080102, 33--38. doi:10.4303/jglta/S080102. https://projecteuclid.org/euclid.jglta/1319028473


Export citation

References

  • M. Gunaydin and F. Gursey. Quark statistics and octonions. Phys. Rev. D9 (1974) 3387-3391.
  • G. Birkhoff and J. von Neumann. The Logic of Quantum Mechanics. Ann. Math. 37 (1936) 823-829.
  • V. Dzhunushaliev. Non-associativity, supersymmetry and hidden variables, J. Math. Phys. 49 (2008) 042108-042117; arXiv: 0712.1647 [quant-ph].
  • M. Gogberashvili. Octonionic electrodynamics, J. Phys. A 39 (2006) 7099-7104; arXiv: hep-th/0512258.
  • M. Gogberashvili. Octonionic version of Dirac equations, Int. J. Mod. Phys. A 21 (2006) 3513-3524; arXiv: hep-th/0505101.
  • V. Dzhunushaliev. Observables and unobservables in a non-associative quantum theory. J. of Gen. Lie Theory Appl. 2 (2008) 269-272; arXiv: quant-ph/0702263.
  • H.C. Myung, Some classes of flexible Lie-admissible algebras. Trans. Amer. Math. Soc. 167 (1972) 79-88.
  • R. Schafer. Introduction to Non-Associative Algebras. Dover, New York, 1995;
  • T. A. Springer and F. D. Veldkamp. Octonions, Jordan Algebras and Exceptional Groups. Springer Monographs in Mathematics, Springer, Berlin, 2000.
  • Susumu Okubo. Introduction to Octonion and Other Non-Associative Algebras in Physics. Cambridge University Press, Cambridge, 1995.
  • J. C. Baez. The Octonions. Bull. Amer. Math. Soc. 39 (2002) 145-205; math.ra/0105155.
  • J. L$\tilde{o}$hmus, E. Paal and L. Sorgsepp. About Nonassociativity in Mathematics and Physics. Acta Appl. Math. 50 (1998) 3-31.