Skip to main content
SpringerLink
Log in

Multivectorial representation of Lie groups

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

Abstract

In vector spaces of dimensionn=p+q a multivector (Clifford) algebraC(p, q) can be constructed. In this paper a multivectorC(p, q) representation, riot restricted to the bivector subalgebraC 2(p, q), is developed for some of the Lie groups more frequently used in physics. This representation should be especially useful in the special cases of (grand) unified gauge field theories, where the groups used do not always have a simple tensor representation.

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

  • Aitchison, I. J. R. (1984).An Informal Introduction to Gauge Field Theories, Cambridge University Press, Cambridge.

    Google Scholar 

  • Artin, E. (1957).Geometric Algebra, Interscience, New York.

    Google Scholar 

  • Bugajska, K. (1986a).Journal of Mathematical Physics,27, 143.

    Google Scholar 

  • Bugajska, K. (1986b).Journal of Mathematical Physics,27, 853.

    Google Scholar 

  • Bugajska, K. (1986c).Journal of Mathematical Physics,27, 2700.

    Google Scholar 

  • Chisholm, J. S. R., and Common, A. K. (1986).Clifford Algebras and Their Applications in Mathematical Physics, Reidel, Dordrecht.

    Google Scholar 

  • Clifford, W. K. (1878).American Journal of Mathematics,1, 350–358.

    Google Scholar 

  • Dauns, J. (1988).International Journal of Theoretical Physics,27, 183.

    Google Scholar 

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

    Google Scholar 

  • Hestenes, D., and Sobczyk, G. (1984).Clifford Algebra to Geometric Calculus, D. Reidel, Dordrecht.

    Google Scholar 

  • Keller, J. (1982).International Journal of Theoretical Physics,21, 829.

    Google Scholar 

  • Keller, J. (1984).International Journal of Theoretical Physics,23, 818.

    Google Scholar 

  • Keller, J. (1985). Generalization of the Dirac equation admitting isospin and color symmetries, inQuantum Theory and Gravitation, III Symposium Loyola University, New Orleans.

  • Keller, J. (1986).International Journal of Theoretical Physics,25, 779.

    Google Scholar 

  • Keller, J. (1991).International Journal of Theoretical Physics,30, 137.

    Google Scholar 

  • Keller, J., and Rodríguez-Romo, S. (1990).Journal of Mathematical Physics,31, 2501.

    Google Scholar 

  • Lounesto, P. (1980).Annales Institut Henri Poincaré, A,33, 11.

    Google Scholar 

  • Rodríguez, S. (1986). Algunos Usos de los Métodos Multivectoriales y Espinoriales en Teoría Cuántica de la Materia, M. Sc. Thesis, F. Q., National University of Mexico.

  • Ross, G. (1985). Grand unified theories,Frontiers in Physics, V-60.

  • Wu, Ki Tung (1985).Group Theory in Physics, World Scientific, Singapore.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. División de Ciencias Básicas, Fac. de Quím., Universidad Nacional Autónoma de México, 04510, México D.F., 70-528, México

    Jaime Keller & Suemi Rodríguez-Romo

  2. Facultad de Estudios Superiores Cuautitlán, Universidad Nacional Autónoma de México, Cuautitlán Izcalli, 54700, Edo. de México, México

    Jaime Keller & Suemi Rodríguez-Romo

Authors
  1. Jaime Keller
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Suemi Rodríguez-Romo
    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

Keller, J., Rodríguez-Romo, S. Multivectorial representation of Lie groups. Int J Theor Phys 30, 185–196 (1991). https://doi.org/10.1007/BF00670711

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00670711

Keywords

Search

Navigation