Harmonic analysis on the timelike and spacelike hyperboloids: Application to inclusive reactions

Abstract

The timelike and spacelike hyperboloids are homogeneous spaces with respect to the Lorentz group, viz. the quotient spaces SL_2,C / SU₂ and SL_2,C / SU_1.1. The scattering amplitude possesses sufficient analyticity to continue from the timelike to the spacelike region. Starting from the harmonic analysis in the SU_1.1 basis for functions defined on the timelike sheet, with the aid of analytic continuation, we deduce the harmonic analysis for functions defined on the spacelike sheet in anSU 2 basis. The mathematical procedure is illustrated in detail by considering the three-body scattering amplitude, which is relevant for a discussion of inclusive reactions.