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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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
- Vector Field
- Electromagnetic Field
- Symmetry Group
- Field Equation
- Generalize Equation