Abstract
The equations describing an electromagnetic field, a Yang-Mills massless field, and a free massive vector field are generalized in a quaternion setting. The generalized equations are invariant under a six-parameter group of transformations, which do not affect the space-time coordinates. In application to the generalized Maxwell equations the indicated group is isomorphic to Zaitsev's group of outer transformations of the electromagnetic field variables.
Similar content being viewed by others
Literature cited
D. P. Zhelobenko, Compact Lie Groups and Their Representations [in Russian], Nauka, Moscow (1970).
Yu. V. Novozhilov, Introduction to the Theory of Elementary Particles [in Russian], Nauka, Moscow (1972).
V. I. Strazhev and L. M. Tomil'chik, Electrodynamics and Magnetic Charge [in Russian], Nauka i Tekhnika, Minsk (1975).
G. A. Zaitsev, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 12 (1969).
G. A. Zaitsev and A. M. Solunin, Izv. Vyssh. Uchebn. Zaved, Fiz., No. 11 (1969).
G. A. Zaitsev, Algebraic Problems in Mathematical and Theoretical Physics [in Russian], Nauka, Moscow (1974).
I. Bialynicki-Birula, Bull. Acad. Polon. Sci.,11, 135 (1963).
S. Mandelstam, Phys. Rev.,175, 1580 (1968).
A. A. Borgardt, Zh. Éksp. Teor. Fiz.,24, No. 24 (1953).
E. Durand, Phys. Rev.D11, 3405 (1975).
A. A. Borgardt, Zh. Éksp. Teor. Fiz.,45, 116 (1963).
A. A. Borgardt, Author's Abstract of Doctoral Dissertation, Minsk (1965).
Author information
Authors and Affiliations
Additional information
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 45–48, August, 1977.
The author is indebted to S. I. Kruglov, Yu. A. Kurochkin, and E. A. Tolkachev for a critical and stimulating discussion of the present results.
Rights and permissions
About this article
Cite this article
Strazhev, V.I. Symmetry group of generalized vector field equations. Soviet Physics Journal 20, 1021–1023 (1977). https://doi.org/10.1007/BF00892827
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00892827