Consistent models of spin 0 and 1/2 extended particles scattering in external fields

  • S. Twareque Ali
  • Eduard Prugovecki
Quantum-Mechanical Scattering Theory
Part of the Lecture Notes in Physics book series (LNP, volume 130)


By replacing sharp with stochastic localizability, positive-definite and covariant probability densities yielding conserved and covariant probability currents can be introduced in relativistic quantum mechanics. The resulting stochastic phase-space formalism can be used to construct covariant models of extended spin 0 and 1/2 particles, whose interaction with an external electromagnetic field leaves the space of positive-energy wave functions invariant.


Magnetic Dipole Moment Relativistic Quantum Mechanic External Electromagnetic Field Lorentz Boost Free Propagator 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A. Pais: in Aspects of Quantum Theory, ed. by A. Salam and E.P. Wigner (Cambridge University Press, Cambridge, 1972)Google Scholar
  2. [2]
    A.S. Wightman: [1], p. 98Google Scholar
  3. [3]
    P.A.M. Dirac: Proc. Roy. Soc. (London) A268, 57 (1962)Google Scholar
  4. [4]
    G. Rosen: Int. J. Theor. Phys. 17, 1 (1978)Google Scholar
  5. [5]
    E. Prugovecki: J. Math. Phys. 19, 2260 (1978)Google Scholar
  6. [6]
    S.T. Ali: J. Math. Phys. 20, 1385 (1979)Google Scholar
  7. [7]
    W. Heisenberg: Am. J. Phys. 43, 389 (1975)Google Scholar
  8. [8]
    E. Prugovecki: Found. Phys. 9, 575 (1979)Google Scholar
  9. [9]
    S.T. Ali, E. Prugovecki: J. Math. Phys. 18, 219 (1977)Google Scholar
  10. [10]
    S.T. Ali, E. Prugovecki: Physica 89A, 501 (1977)Google Scholar
  11. [11]
    E. Prugovecki: Phys. Rev. D 18, 3655 (1978)Google Scholar
  12. [12]
    E. Prugovecki: “Quantum action principle and functional integration over paths in stochastic phase space,” to appearGoogle Scholar
  13. [13]
    S.T. Ali, E. Prugovečki: “Self-consistent relativistic models for extended spin models 1/2 particles in external fields,” to appearGoogle Scholar
  14. [14]
    A.O. Barut: Electrodynamics and Classical Theory of Fields and Particles (MacMillan, New York, 1964)Google Scholar
  15. [15]
    J.M. Lévy-Leblond: Group Theory and Its Applications, Vol. II, ed. by E.M. Loebl (Academic, New York, 1971)Google Scholar
  16. [16]
    C.F. Dietrich: Uncertainty, Calibration, and Probability (Wiley, New York, 1973)Google Scholar
  17. [17]
    E. Prugovecki: Ann. Phys. (N.Y.) 110, 201 (1978)Google Scholar
  18. [18]
    S.T. Ali, E. Prugovecki: Int. J. Theor. Phys. 16, 689 (1977)Google Scholar
  19. [19]
    E. Prugovecki: Physica 91A, 202 (1978)Google Scholar
  20. [20]
    R. Hofstadter: Ann. Rev. Nucl. Sci. 7, 231 (1956)Google Scholar
  21. [21]
    E. Prugovečki: Rep. Math. Phys. (1979–80), to appearGoogle Scholar
  22. [22]
    S.T. Ali: “On some representations of the Poincaré group on phase space II,” to appearGoogle Scholar
  23. [23]
    E. Prugovečki: “A self-consistent approach to quantum field theory for extended particles,” to appearGoogle Scholar
  24. [24]
    P. Gnadig, Z. Kunszt, P. Hasenfratz, G. Koti: Ann. Phys. (N.Y.) 116, 380 (1978)Google Scholar
  25. [25]
    R.P. Feynman, M. Kislinger, F. Ravndal: Phys. Rev. D 3, 2706 (1971)Google Scholar
  26. [26]
    Y.S. Kim, M.E. Noz: Phys. Rev. D 15, 335 (1977)Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • S. Twareque Ali
    • 1
  • Eduard Prugovecki
    • 2
  1. 1.Department of MathematicsUniversity of Prince Edward IslandCharlottetownCanada
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada

Personalised recommendations