Skip to main content
Log in

Hamiltonian structures for homogeneous spaces

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

The definition and classification of classical relativistic particles requires the classification of certain invariant tensor fields on the inhomogeneous Lorentz group. The entire 10-parameter set is exhibited. At the same time, a much larger class of Lie groups is treated. The connection with particles will be presented in the succeeding article.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bargmann, V., Wigner, E. P.: Group-theoretical discussion of relativistic wave equations, Proc. Natl. Acad. Sci. U.S.34, 211–223 (1948).

    Google Scholar 

  2. Chevalley, C.: Lie groups, Princeton U.P. 1946.

  3. —— Eilenberg, S.: Cohomology theory of Lie groups and Lie algebras, Trans. Am. Math. Soc.63, 85–124 (1948).

    Google Scholar 

  4. Helgason, S.: Differential geometry and symmetric spaces. New York: Academic Press 1962.

    Google Scholar 

  5. Sternberg, S.: Differential geometry. Englewood Cliffs, N. Jersey: Prentice Hall 1964.

    Google Scholar 

  6. Arens, R.: Invariant sublogics as a way from scalar to manycomponent wave equations, J. Math. Mech.15, 344–372 (1966).

    Google Scholar 

  7. —— A quantum-dynamical relativistically-invariant rigid body system, Trans. Am. Math. Soc.147, 153–201 (1970).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Arens, R. Hamiltonian structures for homogeneous spaces. Commun.Math. Phys. 21, 125–138 (1971). https://doi.org/10.1007/BF01646747

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01646747

Keywords

Navigation