Skip to main content
SpringerLink
Log in

Spinors in the Lorentz group and their implications for quantum mechanics

  • Regular Article - Theoretical Physics
  • Published:
The European Physical Journal C Aims and scope Submit manuscript

An Erratum to this article was published on 04 June 2008

An Erratum to this article was published on 04 June 2008

Abstract

We investigate what the precise meaning is of a spinor in the rotation and Lorentz groups. We find that spinors correspond to a special coding of a group element. This is achieved by coding the whole reference frame into a special isotropic or “zero-length” vector. The precise form of that special vector in the Lorentz group is lacking in the literature, and this leads to some confusion, as the point that the coding can be complete has been missed. We then apply these ideas to quantum mechanics and find that the Dirac equation can be derived by just trying to describe a rotating electron.

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

  1. G. Coddens, Eur. J. Phys. 23, 549 (2002), but of course the following references are much more important

    Article  MathSciNet  MATH  Google Scholar 

  2. E. Cartan, The Theory of Spinors (Dover, New York, 1981)

    MATH  Google Scholar 

  3. J. Hladik, Les Spineurs en Physique (Masson, Paris, 1996)

    Google Scholar 

  4. R. Penrose, W. Rindler, Spinors and Space-Time, Vol. I, Two-spinor Calculus and Relativistic Fields (Cambridge University Press, Cambridge, 1984)

    Google Scholar 

  5. V. Smirnov, Cours de Mathémathiques Supérieures, Vol. 2 and 3 (Mir, Moscow, 1972)

    Google Scholar 

  6. C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation (Freeman, San Francisco, 1970)

    Google Scholar 

  7. J.F. Cornwell, Group Theory in Physics (Academic Press, Londen, 1984)

    MATH  Google Scholar 

  8. S. Sternberg, Group Theory in Physics (Cambridge University Press, Cambridge, 1994)

    Google Scholar 

  9. H.F. Jones, Groups, Representations and Physics (Adam Hilger, Bristol, 1990)

    Google Scholar 

  10. M. Chaichian, R. Hagedorn, Symmetries in Quantum Mechanics, From Angular Momentum to Supersymmetry (IOP, Bristol, 1998)

    MATH  Google Scholar 

  11. T. Inui, Y. Tanabe, Y. Onodera, Group Theory and its Applications in Physics (Springer, Heidelberg, 1990)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire des Solides Irradiés, Ecole Polytechnique, CEA/DSM/IRAMIS, CNRS, Route de Saclay, 91128, Palaiseau Cedex, France

    G. Coddens

Authors
  1. G. Coddens
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. Coddens.

Additional information

PACS

02.20.-a; 03.65.-w; 03.65.Fd

An erratum to this article can be found at http://dx.doi.org/10.1140/epjc/s10052-008-0636-0

Rights and permissions

Reprints and permissions

About this article

Cite this article

Coddens, G. Spinors in the Lorentz group and their implications for quantum mechanics. Eur. Phys. J. C 55, 145–157 (2008). https://doi.org/10.1140/epjc/s10052-008-0563-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjc/s10052-008-0563-0

Keywords

Search

Navigation