Skip to main content
SpringerLink
Log in

Nature's natural numbers: relativistic quantum theory over the ring of complex quaternions

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

The 2×2 complex matrix formulation of relativity and the two-component spin-1/2 formalism are merged with the complex quaternion algebra to yield a concise, manifestly covariant formalism of relativistic quantum mechanics. Along with reproducing all the old results of quantum theory, this complex quaternion formulation extends naturally the concept of scalar mass by adding to it orientation- and velocity-dependent parts giving a hyper-mass. The hyper-mass spin-1/2 equation, with the scalar part of the mass set equal to zero, gives a subtle variation on the two-component neutrino theory with very unsubtle consequences, such as an invariant mass parameter which could distinguishv eandv μ and elimination of the superposition principle.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Allcock, G. R. (1961).Nuclear Physics,27, 204.

    Google Scholar 

  • Biedenharn, L. C. Han, M. Y. and van Dam, H. (1971).Physics Review Letters,27, 1167.

    Google Scholar 

  • Birkhoff, G. and von Neumann, J. (1936).Annals of Mathematics,37, 823.

    Google Scholar 

  • Bork, A. M. (1966).American Journal of Physics,34, 202.

    Google Scholar 

  • Brand, L. (1947).Vector and Tensor Analysis. Wiley, New York.

    Google Scholar 

  • Brown, L. M. (1962). In:Lectures in Theoretical Physics, Vol. IV. Interscience, New York.

    Google Scholar 

  • Carruthers, P. (1966).Introduction to Unitary Symmetry. Interscience, New York.

    Google Scholar 

  • Condon, V. E. and Shortley, G. H. (1935).The Theory of Atomic Spectra. Cambridge University Press, London.

    Google Scholar 

  • Conway, A. W. (1937).Proceedings of the Royal Society of London,A162, 145.

    Google Scholar 

  • Dyson, F. J. (1962).Journal of Mathematics and Physics,3, 1199.

    Google Scholar 

  • Emch, G. (1963).Helvetica physica acta,36, 739, 770 (in French).

    Google Scholar 

  • Finkelstein, D., Jauch, J. M., Schiminovich, S. and Speiser, D. (1962a).Journal of Mathematics and Physics,3, 207.

    Google Scholar 

  • Finkelstein, D., Jauch, J. M., Schiminovich, S. and Speiser, D. (1962b).Helvetica physica acta,35, 328.

    Google Scholar 

  • Finkelstein, D., Jauch, J. M., Schiminovich, S. and Speiser, D. (1963).Journal of Mathematics and Physics,4, 136, 788.

    Google Scholar 

  • Gürsey, F. (1956a).Nuovo cimento,3, 988.

    Google Scholar 

  • Gürsey, F. (1956b).Revue de la Faculté des sciences de l'Université d'Istanbul,A20, 149.

    Google Scholar 

  • Gürsey, F. (1956c).Revue de la Faculté des sciences de l'Université d'Istanbul,A21, 33.

    Google Scholar 

  • Gürsey, F. (1958).Nuovo cimento,7, 411.

    Google Scholar 

  • Hestenes, D. O. (1966).Space-Time Algebras. Gordon and Breach, New York.

    Google Scholar 

  • Hestenes, D. O. (1968).Journal of Mathematical Analysis and Applications,24, 313, 467.

    Google Scholar 

  • Hestenes, D. O. (1971).American Journal of Physics,39, 1028.

    Google Scholar 

  • Jenč, F. (1966).Czechoslovak Journal of Physics, B,16, 555.

    Google Scholar 

  • Jordan, P. (1968).Communications in Mathematical Physics,9, 279 (in German).

    Google Scholar 

  • Kaneno, T. (1960).Progress of Theoretical Physics,23, 17.

    Google Scholar 

  • Klein, F. (1911).Physik Zeitschrift,12, 17.

    Google Scholar 

  • Lanczos, C. (1929).Physik Zeitschrift,57, 447, 474, 484.

    Google Scholar 

  • MacFarlane, A. J. (1962).Journal of Mathematics and Physics,3, 1116.

    Google Scholar 

  • Misra, S. P. (1960).Progress of Theoretical Physics,23, 1.

    Google Scholar 

  • Naimark, M. A. (1964).Linear Representations of the Lorentz Group. Pergamon Press, New York.

    Google Scholar 

  • Natarajan, S. and Viswanath, K. (1967).Journal of Mathematics and Physics,8, 582.

    Google Scholar 

  • Newman, E. T. and Penrose, R. (1962).Journal of Mathematics and Physics,3, 566.

    Google Scholar 

  • Pais, A. (1961).Physical Review Letters,7, 291.

    Google Scholar 

  • Penney, R. (1968).American Journal of Physics,36, 871.

    Google Scholar 

  • Phipps, T. E., Jr. (1960).Physical Review,118, 1653.

    Google Scholar 

  • Rastall, P. (1964).Reviews of Modern Physics,36, 820.

    Google Scholar 

  • Sachs, M. (1968).Nuovo cimento,LIIIB, 398.

    Google Scholar 

  • Sachs, M. (1970).Nuovo cimento,LXVIB, 137.

    Google Scholar 

  • Schiff, L. (1955).Quantum Mechanics, p. 334. McGraw-Hill, New York.

    Google Scholar 

  • Schremp, E. J. (1959).Physics Reviews,99, 1603.

    Google Scholar 

  • Silberstein, L. (1924).The Theory of Relativity. Macmillan, London.

    Google Scholar 

  • Streater, R. F. and Wightman, A. S. (1964).PCT, Spin and Statistics, and All That. Benjamin, New York.

    Google Scholar 

  • Tiomno, J. (1963).Theoretical Physics. International Atomic Energy Agency, Vienna.

    Google Scholar 

  • Winans, J. G. (1962).American Journal of Physics,36, 820.

    Google Scholar 

  • Yang, C. N. and Mills, R. L. (1954).Physical Review,96, 191.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, California Western College, 92106, San Diego, California

    James D. Edmonds Jr.

Authors
  1. James D. Edmonds Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Edmonds, J.D. Nature's natural numbers: relativistic quantum theory over the ring of complex quaternions. Int J Theor Phys 6, 205–224 (1972). https://doi.org/10.1007/BF00672074

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00672074

Keywords

Search

Navigation