Abstract
Some new classical solutions of the sourceless SO(4,1) gauge field equations are found by identifying the internal symmetry indices with the space-time indices as in the cases of the instanton or the meron solutions. This identification of the internal and the space-time indices takes the simplest form when the gauge field equation is expressed in (4,1) de Sitter space, which is conformal to the Minkowski space having the de Sitter group SO(4,1) as a group of motions. The form of the solutions is close to the de Sitter ‘plane wave’ solutions found recently, i.e. the solutions of the Klein-Gordon, Dirac and Maxwell-Proca equations in de Sitter space. The group theoretical structure of the new solutions is discussed and their relations to the Iwasawa decomposition of the non-compact semisimple group SO(4,1) are pointed out.
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