Soviet Physics Journal

, Volume 32, Issue 10, pp 840–845 | Cite as

Secondary quantization of the Dirac free field in hypercomplex system of numbers

  • D. F. Kurdgelaidze
Elementary Particle Physics and Field Theory


The method of secondary quantization of the Dirac free field is developed in the formalism of a hypercomplex system of numbers, generalizing the Clifford algebra to state space analogously to its generalization to distorted space. Then, after conversion to a new basis, it is shown that, taking account of the projection operators, the bases of Fermi algebra — creation and annihilation operators — may be taken as the new basis. Writing the solution of the Dirac free equation in the new basis, the physically observed field values are written in terms of secondary-quantization operators. The adjustable Dirac-field function is calculated in the same formalism.


State Space Projection Operator Annihilation Operator Clifford Algebra Free Field 
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Literature cited

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    D. F. Kurdgelaidze, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 11, 22 (1986); No. 12, 58 (1986); D. F. Kurdgelaidze, Acta Phys. Hung.,57(1–2), 79 (1985).Google Scholar
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    N. N. Bogolyubov, Zh. Éksp. Teor. Fiz.,34, 73 (1958); N. N. Bogolyubov and N. N. Bogolyubov, Jr., Introduction to Quantum Statistical Mechanics [in Russian], Nauka, Moscow (1986).Google Scholar
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    S. V. Tyablikov, Methods of Quantum Theory of Magnetism [in Russian], Nauka, Moscow (1975).Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • D. F. Kurdgelaidze
    • 1
  1. 1.Tbilisi InstituteUSSR

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