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Symmetry group of generalized vector field equations

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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.

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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.

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Strazhev, V.I. Symmetry group of generalized vector field equations. Soviet Physics Journal 20, 1021–1023 (1977). https://doi.org/10.1007/BF00892827

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Keywords

  • Vector Field
  • Electromagnetic Field
  • Symmetry Group
  • Field Equation
  • Generalize Equation