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Commuting Nonselfadjoint Operators and a Unified Theory of Waves and Corpuscles

  • M. S. Livšic
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 98)

Abstract

In this paper, which is closely connected with our previous study ”What is a particle from the standpoint of systems theory?” [3], we consider the case of pairs of commuting operators with one-dimensional imaginary parts and we develop a unified theory of waves and particles for the case of Dirac equations. Particles emerge in Space as localized fields with singularities at their centers and wave equations appear as compatibility conditions for an overdetermined pair of equations of corresponding open systems.

Keywords

Open Field Dirac Equation Transition Index Blaschke Product Channel Vector 
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References

  1. 1.
    N.I. Akhieser and I.M. Glazman: Theory of Linear Operators in Hilbert Space, Pitman Advanced Publishing Program, London, 1980.Google Scholar
  2. 2.
    Louis de Broglie: Non-Linear Wave Mechanics. Elsevier, Amsterdam, 1960.Google Scholar
  3. 3.
    M.S. Livšic: What is a Particle from the Standpoint of Systems Theory?, Integral Equations Operator Theory, 14 (1991), 552–563.MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    M.S. Livsic: Commuting Nonselfadjoint Operators and Collective Motions of Systems, in ”Commuting Nonselfadjoint Operators in Hilbert Space”, Lecture Notes in Math., 1272, Springer-Verlag, 1987.Google Scholar
  5. 5.
    M.S. Livsic and A.A. Jancevich: Theory of Operator Colligations in Hilbert Space, J. Wiley, New York, 1979.Google Scholar
  6. 6.
    Nicholas Rescher: G.W.Leibniz’s Monadology (an edition for students), London, 1991.Google Scholar

Copyright information

© Springer Basel AG 1997

Authors and Affiliations

  • M. S. Livšic
    • 1
  1. 1.Department of Mathematics and Computer SciencesBen-Gurion University of the NegevBeer-ShevaIsrael

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