MANIFESTLY COVARIANT FORMS FOR LORENTZ GROUP UNITARY REPRESENTATIONS

We show that the unitary irreducible representations (UIRs) of the pro per homogeneous Lorentz group SO(3,1) can be realized in a manifestly covariant form, using Hilbert spaces of functions on suitable geometri cal configurations of vectors in space time. The concept and propertie s of isotropic lines, which are generators of spacelike hyperboloids, and of stability groups of lightlike vectors, are crucial to the const ructions. Both principal and supplementary Series UIRs are treated. (C ) 1995 American Institute of Physics.