All JournalsPhysics Magazine

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

On the Formal Extension of Dirac's Equation under Continuous Transformation Groups

E. L. Hill

  • Department of Physics, University of Minnesota, Minneapolis, Minnesota

Phys. Rev. 73, 910 – Published 15 April, 1948

DOI: https://doi.org/10.1103/PhysRev.73.910

Abstract

The theory of equations of the Dirac type which are form-invariant under general finite continuous groups of point transformations in space-time is developed. The possible equations invariant under a given group depend on the structure of the group, but in each case the required invariance imposes a set of linear homogeneous relations on the β-operators with which any assumed algebra must be consistent. It is shown that the algebra appropriate to the general equation possessing form-invariance under the inhomogeneous Lorentz group is necessarily of infinite order.

References (14)

  1. H. C. Corben and J. Schwinger, Phys. Rev. 58, 953 (1940)
  2. J. H. Bartlett, Phys. Rev. 72, 219 (1947)
  3. W. Pauli, Rev. Mod. Phys. 13, 203 (1941)
  4. H. J. Bhabha, Rev. Mod. Phys. 17, 200 (1945)
  5. Harish-Chandra, Phys. Rev. 71, 793 (1947)
  6. A. H. Taub, Phys. Rev. 51, 512 (1937)
  7. E. Schrödinger, Proc. Roy. Irish Acad. A46, 25 (1940)
  8. L. Infeld and A. Schild, Phys. Rev. 70, 410 (1946)
  9. E. L. Hill, Phys. Rev. 67, 358 (1945) ibid.72, 143 (1947)
  10. P. A. M. Dirac, Ann. Math. [2] 37, 429 (1936)
  11. H. J. Bhabha, Proc. Camb. Phil. Soc. 32, 622 (1936)
  12. L. P. Eisenhart, Continuous Groups of Transformations, (Princeton University Press, Princeton, 1933)
  13. [12], Section 35
  14. Omitted endnote

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation