Advertisement

The Dirac Equation

  • Walter T. GrandyJr.
Part of the Fundamental Theories of Physics book series (FTPH, volume 41)

Abstract

For almost 100 years a major goal of physics has been to understand the electron. Although such a desire may not seem excessive, it nevertheless is far from being realized on a fundamental level. A great deal of the effort that has been expended in the classical domain is reviewed in the Appendix, where we see that only the nonrelativistic, finite-size model appears to be completely well behaved. [Some recent progress has been booked, however, in the covariant formulation of an extended model [e.g., Schwinger (1983), Beil (1989).] Yet all experimental evidence still fails to reveal any structure for the particle. Whether or not one has faith in the ultimate existence of point particles, that is what is currently indicated by the data. Lacking any experimental definition or direction to the contrary, that is also the generally accepted model today, and the one we shall continue to follow for the moment in the quantum domain.

Keywords

Commutation Relation Dirac Equation Rest Frame Lorentz Transformation Dirac Particle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anderson, C.D.: 1933, ‘Positive Electron’, Phys. Rev. 43, 491.ADSGoogle Scholar
  2. Barut, A.O., and A.J. Bracken: 1981a, ‘Zitterbewegung and the Internal Geometry of the Electron’, Phys. Rev. D 23, 2454.MathSciNetADSGoogle Scholar
  3. Barut, A.O., and A.J. Bracken: 1981b, ‘Magnetic-Moment Operator of the Relativistic Electron’, Phys. Rev. D 24, 3333.MathSciNetADSGoogle Scholar
  4. Barut, A.O., and R. Rączka: 1986, Theory of Group Representations and Applications, 2nd ed., World Scientific, Singapore.zbMATHGoogle Scholar
  5. Beil, R.G.: 1989, ‘The Extended Classical Charged Particle’, Found. Phys. 19, 319.MathSciNetADSGoogle Scholar
  6. Bromberg, J.: 1976, ‘The Concept of Particle Creation before and after Quantum Mechanics’, in R. McCormmach (ed.), Historical Studies in the Physical Sciences, Vol.17, Princeton University Press, Princeton.Google Scholar
  7. Chamberlain, O., E. Segrè, C. Wiegand, and T. Ypsilantis: 1955, ‘Observation of Antiprotons’, Phys. Rev. 100, 947.ADSGoogle Scholar
  8. Crawford, J.P.: 1985, ‘On the Algebra of Dirac Bispinor Densities: Factorization and Inversion Theorems’, J. Math. Phys. 26, 1439.MathSciNetADSGoogle Scholar
  9. Crawford, J.P.: 1987, ‘Bispinor Geometry in Two Spacetime Dimensions’, Proc. Penn. Acad. Sci. 61, 202.Google Scholar
  10. Dirac, P.A.M.: 1928, ‘The Quantum Theory of the Electron’, Proc. Roy. Soc. (London) A117, 610.ADSGoogle Scholar
  11. Dirac, P.A.M.: 1930, ‘A Theory of Electrons and Protons’, Proc. Roy. Soc. (London) A126, 360.ADSGoogle Scholar
  12. Dirac, P.A.M.: 1977. The Relativistic Electron Wave Equation, Europhysics News, October.Google Scholar
  13. Foldy, L., and S. Wouthuysen: 1950, ‘On the Dirac Theory of Spin 1/2 Particles and Its Non-Relativistic Limit’, Phys. Rev 78, 29.ADSzbMATHGoogle Scholar
  14. Good, R.H., Jr.: 1955, ‘Properties of the Dirac Matrices’, Rev. Mod. Phys. 27, 187.MathSciNetADSzbMATHGoogle Scholar
  15. Gordon, W.: 1928, ‘Der Strom der Diracschen Elektronentheorie’, Z. Phys. 50, 630.ADSzbMATHGoogle Scholar
  16. Hegerfeldt, G.C.: 1974, ‘Remark on Causality and Particle Localization’, Phys. Rev. D 10, 3320.ADSGoogle Scholar
  17. Hestenes, D.: 1986, ‘Clifford Algebra and the Interpretation of Quantum Mechanics’, in J.S.R. Chisholm and A.K. Common (eds.), Clifford Algebras and Their Applications in Mathematical Physics, Reidel, Dordrecht, p.321.Google Scholar
  18. Hirshfeld, A.C., and F. Metzger: 1986, ‘A Simple Formula for Combining Rotations and Lorentz Boosts’, Am. J. Phys. 54, 550.MathSciNetADSGoogle Scholar
  19. Huang, K.: 1952, ‘On the Zitterbewegung of the Dirac Electron’, Am. J. Phys. 20, 479.ADSzbMATHGoogle Scholar
  20. Kaloyerou, P.N.: 1988, ‘Comments on the Hegerfeldt “Paradox” ’, Phys. Lett. A 129, 285.MathSciNetADSGoogle Scholar
  21. Kim, Y.S., and M.E. Noz: 1986, Theory and Applications of the Poincaré Group, Reidel, Dordrecht.Google Scholar
  22. Klein, O.: 1929, ‘Die Reflex von Elektronen an einen Potentialsprung nach der relativistischen Dynamik von Dirac’, Z. Phys. 53, 157.ADSzbMATHGoogle Scholar
  23. Kobe, D.H.: 1978, ‘Derivation of Maxwell’s Equations from the Local Gauge Invariance of Quantum Mechanics’, Am. J. Phys. 46, 342.MathSciNetADSGoogle Scholar
  24. Moyer, D.F.: 1981a, ‘Origins of Dirac’s Electron, 1925–1928’, Am. J. Phys. 49, 944.ADSGoogle Scholar
  25. Mover, D.F.: 1981b, ‘Evaluations of Dirac’s Electron, 1928–1932’, Am. J. Phys. 49, 1055.ADSGoogle Scholar
  26. Mover, D.F.: 1981c, ‘Vindications of Dirac’s Electron, 1932–1934’, Am. J. Phys. 49, 1120.ADSGoogle Scholar
  27. Newton, T.D., and E.P. Wigner: 1949, ‘Localized States for Elementary Systems’, Rev. Mod. Phys. 21, 400.ADSzbMATHGoogle Scholar
  28. Oppenheimer, J.R.: 1930, ‘On the Theory of Electrons and Protons’, Phys. Rev. 35, 562.ADSGoogle Scholar
  29. Pauli, W.: 1936, ‘Contributions mathématiques à la théorie des matrices de Dirac’, Ann. Inst. Henri Poincaré 6, 109.MathSciNetGoogle Scholar
  30. Sauter, F.: 1931, ‘Über des verhalten eines Elektrons im homogenen elektrischen Feld nach der relativistischen Theorie Dirac’s’, Z. Phys. 69, 742.ADSGoogle Scholar
  31. Schrödinger, E.: 1930, ‘Über die Kräftefreie Bewegung in der relativistischen Quantenmechanik’, Sitzber. preuss. Akad. Wiss. Physik-math. Kl. 24, 418.Google Scholar
  32. Schwinger, J.: 1983, ‘Electromagnetic Mass Revisited’, Found. Phys. 13, 373.MathSciNetADSGoogle Scholar
  33. Weyl, H.: 1931, Gruppentheorie und Quantenmechanik, 2nd ed., S. Hirzel, Leipzig.Google Scholar
  34. Wightman, A.S.: 1962, ‘On the Localizability of Quantum Mechanical Systems’, Rev. Mod. Phys. 34, 845.MathSciNetADSGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1991

Authors and Affiliations

  • Walter T. GrandyJr.
    • 1
  1. 1.Department of Physics and AstronomyUniversity of WyomingUSA

Personalised recommendations