Second Quantization of the Dirac Field and Definition of the Vacuum

  • Walter Greiner
  • Berndt Müller
  • Johann Rafelski


Chapter 6 treated at length the instability of the neutral Dirac vacuum in a sufficiently strong, i.e. supercritical, external field and its spontaneous decay into a charged vacuum. The discussion then was based on Dirac’s intuitive hole picture of the electron — positron vacuum combined with the theory of spontaneous autoionization processes. While such an amalgamation of intuitive, pictorial ideas and relativistic quantum mechanics may serve as a useful guide to the underlying physical phenomena, it is equally clear that it cannot rigorously prove our assertions. This proof should more properly be sought within the framework of relativistic quantum field theory which enables a consistent description of processes involving virtual and real particle creation.


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  1. Schw 58.
    J. Schwinger (ed.): Quantum Electrodynamics (Dover, New York 1958)MATHGoogle Scholar
  2. Schw 61.
    S. S. Schweber: Relativistic Quantum Field Theory (Hagler and Row, New York 1961)Google Scholar
  3. Ra 74.
    J. Rafelski, B. Müller, W. Greiner: Nucl. Phys. B68, 585 (1974)CrossRefADSGoogle Scholar
  4. Fu 73a.
    L. Fulcher, A. Klein: Phys. Rev. D8, 2455 (1973)ADSGoogle Scholar
  5. Fu 74.
    L. Fulcher, A. Klein: Ann. Phys. (N.Y.) 84, 335 (1974)CrossRefADSGoogle Scholar
  6. Mü 83a.
    B. Müller: In [Gr 83a] p. 41Google Scholar
  7. Schw 51.
    J. Schwinger: Phys. Rev. 82 664 (1951)CrossRefMATHADSMathSciNetGoogle Scholar
  8. Schw 54.
    J. Schwinger: Phys. Rev. 94 1362 (1954)CrossRefADSMathSciNetGoogle Scholar
  9. Pl 85.
    G. Plunien: Diploma Thesis, Frankfurt University (1983), to be published in Physics ReportsGoogle Scholar
  10. Fr 52.
    J. Friedel: Philos. Mag. 43 153 (1952)MATHGoogle Scholar
  11. Mü 76a.
    B. Müller: Ann. Rev. Nucl. Sci. 26, 351 (1976)CrossRefADSGoogle Scholar
  12. Gr 83e.
    B. Grossman: Phys. Rev. Lett. 50, 464 (1983); ibid. 51 959 (1983)CrossRefADSMathSciNetGoogle Scholar
  13. Ya 83.
    H. Yamagishi: Phys. Rev. D27, 2383 (1983)ADSMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Walter Greiner
    • 1
  • Berndt Müller
    • 1
  • Johann Rafelski
    • 2
  1. 1.Institut für Theoretische PhysikJohann-Wolfgang-Goethe UniversitätFrankfurt/MainFed. Rep. of Germany
  2. 2.Institute of Theoretical Physics and AstrophysicsUniversity of Cape TownRondeboschSouth Africa

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