Foundations of Physics

, Volume 26, Issue 11, pp 1441–1455 | Cite as

Relativistic quantum mechanics of spin-0 and spin-1 bosons

  • Partha Ghose


It is shown that below the threshold of pair creation, a consistent quantum mechanical interpretation of relativistic spin-0 and spin-1 particles (both massive and mussless) ispossible based an the Hamiltonian-Schrödinger form of the firstorder Kemmer equation together with a first-class constraint. The crucial element is the identification of a conserved four-vector current associated with the equation of motion, whose time component is proportional to the energy density which is constrainedto be positive definite for allsolutions. Consequently, the antiparticles must be interpreted as positive-energy states traveling backward in time. This also makes it possible to define hermitian position operators with localized eigensolutions (δ-functions) as well as Bohmian trajectories for bosons. The exact theory is obtained by “second quantization” and is mathematically completely equivalent to conventional quantum field theory. The classical field emerges in the high mean number limit of coherent states of the exact theory. The formalism provides a new basis for computing tunneling times for photons and chaotic phenomena in optics.


Energy Density Coherent State Classical Field Exact Theory Pair Creation 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    N. Kemmer.Proc. R. Soc. London A 173, 91 (1939).Google Scholar
  2. 2.
    P. Ghose, D. Home, and M. N. Sinha Roy.Phys. Lett. A 183, 267 (1993).Google Scholar
  3. 3.
    E. Schrödinger.Proc. R. Soc. London A 229, 39 (1955).Google Scholar
  4. 4.
    This constraint on the energy density and its implications for the antiparticle have not been taken into account in Refs. 1 and 6.Google Scholar
  5. 5.
    T. D. Newton and E. P. Wigner.Rev. Mod. Phys. 21, 400 (1949).Google Scholar
  6. 6.
    P. Ghose and D. Home.Phys. Lett. A 191, 362 (1994).Google Scholar
  7. 7.
    D. Bohm and B. J. Hiley,The Undivided Universe (Routledge. London. 1993). pp. 234–235.Google Scholar
  8. 8.
    P. R. Holland,The Quantum Theory of Motion (Cambridge University Press, Cambridge, 1993), Chap. 12.Google Scholar
  9. 9.
    Harish-Chandra,Proc. R. Soc. London 186, 502 (1946).Google Scholar
  10. 10.
    For the same result in a more general representation, see Ref. 9..Google Scholar
  11. 11.
    E. J. Squires, private communication.Google Scholar
  12. 12.
    A. Einstein.Ann. Phys. (Leipzig) 17, 132 (1905).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Partha Ghose
    • 1
  1. 1.Theoretical Physics DepartmentIndian Association for the Cultivation of ScienceCalcuttaIndia

Personalised recommendations