Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 4 (2008), 063, 4 pages      arXiv:0809.2174      https://doi.org/10.3842/SIGMA.2008.063
Contribution to the Special Issue “Élie Cartan and Differential Geometry”

Exterior Differential Systems for Yang-Mills Theories

Frank B. Estabrook
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA

Received July 18, 2008, in final form September 03, 2008; Published online September 12, 2008

Abstract
Exterior differential systems are given, and their Cartan characters calculated, for Maxwell and SU(2)-Yang-Mills equations in dimensions from three to six.

Key words: exterior differential systems; Cartan characters; Maxwell equations; SU(2)-Yang-Mills equations.

pdf (138 kb)   ps (113 kb)   tex (7 kb)

The Mathematica suite of programs AVF (Algebra Valued Forms) by H.D. Wahlquist:   source (208 kb)

References

  1. Estabrook F.B., Hermann R., Wahlquist H.D., Appendix D, in Hermann R., Yang-Mills, Kaluza-Klein and the Einstein Program, Interdisciplinary Mathematics, Vol. XIX, Math Sci Press, Brookline, Mass., 1978.
  2. Hermann R., Differential form methods in the theory of variational systems and Lagrangian field theories, Acta Appl. Math. 12 (1998), 35-78.
  3. Estabrook F.B., Conservation laws for vacuum tetrad gravity, Classical Quantum Gravity 23 (2006), 2841-2848, gr-qc/0508081.
  4. Estabrook F.B., Mathematical structure of tetrad equations for vacuum relativity, Phys. Rev. D 71 (2005), 044004, 5 pages, gr-qc/0411029.
  5. Hojman S., Problem of the identical vanishing of Euler-Lagrange derivatives in field theory, Phys. Rev. 27 (1983), 451-453.
  6. Betounes D.E., Extension of the classical Cartan form, Phys. Rev. D 29 (1984), 599-606.
  7. Bryant R., Griffiths P., Grossman D., Exterior differential systems and Euler-Lagrange partial differential equations, The University of Chicago Press, Chicago - London, 2003.
  8. Wahlquist H.D., Monte Carlo calculation of Cartan characters, in Proceedings of the International Conference of Aspects of General Relativity and Mathematical Physics, Editors N. Breton, R. Capovilla and T. Matos, Ediciones CINVESTAV, Mexico DF, 1994, 168-174.
  9. Schwinger J., DeRaad L.L. Jr., Milton K.A., Tsai W.-Y., Classical electrodynamics, Westview Press, Boulder CO, 1998.

Previous article   Next article   Contents of Volume 4 (2008)