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

Abstract

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.

Keywords

State Space Projection Operator Annihilation Operator Clifford Algebra Free Field 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    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
  2. 2.
    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
  3. 3.
    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

Personalised recommendations