Wigner Coefficients for the R4 Group and Some Applications

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Abstract
The local isomorphism of the R4 group to the group R3×R3 is utilized to obtain R4 Wigner coefficients for those representations in which the subgroup R3 is diagonal. The R4 Wigner coefficients so defined are then used to obtain recursion relations and differential equations for the representation coefficients, when the group is parametrized appropriately. The R4 spherical harmonics, and their properties, are explicitly obtained as specializations of the general formulas. Physical application to the problem of geometrizing the Coulomb field is briefly discussed.

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