Clebsch-Gordan problem and coefficients for the three-dimensional Lorentz group in a continuous basis. I

Abstract

We have described a new approach to the Clebsch-Gordan problem for the unitary representations of the three-dimensional Lorentz group. We relate the various types of Clebsch-Gordan series to problems in the representation theory of four-dimensional orthogonal and pseudo-orthogonal groups, and thereby achieve a new and better understanding of the structures of the series. At the same time, the Clebsch-Gordan coefficients in a continuous basis are calculated. In this, the first of four papers, the case D⁺⊗D⁺ is worked out in detail.