The SU(u,v)-group path integration

Abstract
Path integration over the SU(u,v) group manifolds, in particular SU(n) and SU(n−1,1), are calculated in an appropriate polar coordinate representation, giving explicitly their set of harmonic functions of all irreducible representations and the corresponding energy spectrum. A path integral identity for multidimensional generalizations of the Pöschl–Teller potential is also stated.