REDUCTION OF RELATIVISTIC WAVEFUNCTIONS TO THE IRREDUCIBLE REPRESENTATIONS OF THE INHOMOGENEOUS LORENTZ GROUP. PART II. ZERO-MASS COMPONENTS.

In a previous paper, we showed how wavefunctions which transform in a relativistic manner in configuration space can be expanded in terms of amplitudes, which for nonzero mass transform like the wavefunctions for irreducible representations of the proper, orthochronous, inhomogeneous Lorentz group. A simple algorithm was given to obtain the expansion. In the present paper, we extend the results to include zero‐mass amplitudes. It is shown that for wavefunctions which are required to transform under the homogeneous Lorentz group such that the matrices which involve the spinor indices are finite dimensional, the zero‐mass amplitudes transform under nonunitary representations of the inhomogeneous Lorentz group. However, it is possible to split up each such nonunitary representation into a part which corresponds to a unitary representation for finite spin and into a part which corresponds to an unphysical change of wavefunction. As examples of the technique, we consider wavefunctions which transform as an ant...