Hostname: page-component-77c89778f8-swr86 Total loading time: 0 Render date: 2024-07-17T08:43:00.314Z Has data issue: false hasContentIssue false
  • English
  • Français

Factorization of the algebra of particles of half-odd spin

Published online by Cambridge University Press:  24 October 2008

K. J. Le Couteur
K. J. Le Couteur
Affiliation:
Department of Theoretical PhysicsThe UniversityLiverpool
Get access Rights & Permissions [Opens in a new window]

Abstract

It is proved that the matrix algebra for any relativistic wave equation of half-odd integral spin can be factorized as the direct product of a Dirac algebra and another, called a ξ-algebra. The structure and representation of ξ-algebras are studied in detail. The factorization simplifies calculations with particles of spin > ½, because the ξ-algebra contains only one-sixteenth as many elements as the original matrix algebra.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 48 , Issue 1 , January 1952 , pp. 110 - 117
Copyright
Copyright © Cambridge Philosophical Society 1952

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Bhabha, J. H.Rev. mod. Phys. 17 (1945), 200.CrossRefGoogle Scholar
(2)Le Couteur, K. J.Proc. Gamb. phil. Soc. 44 (1948), 63.CrossRefGoogle Scholar
(3)Le Couteur, K. J.Proc. roy. Soc. A, 202 (1950), 284.Google Scholar
(4)Le Couteur, K. J.Proc. roy. Soc. A, 202 (1950), 394.Google Scholar
(5)Madhavarao, B. S., Thiruvenkatachar, V. R. and Venkatachaliengar, K.Proc. roy. Soc. A, 187 (1946), 385.Google Scholar