Quantum Theory of the Generalized Wave Equations. I

We have made a systematic analysis of the quantum theory of the infinite‐component fields that transform under the combined representations of SL(2, C)( Majorana )⊗ Dirac . A complete set of solutions of the wave equation includes solutions with timelike and spacelike momenta. We have explicitly calculated the mass spectra for the timelike and spacelike cases. Our method makes use of the decomposition of the product representation into reducible representations of the ``little'' groups SU(2) and SU(1, 1). Finally, the quantization of the generalized fields is presented.