Infinite-Dimensional Representations of the Lorentz Group

Abstract

The method used by Naimark to obtain symmetrical spinors and their transformation law from finite‐dimensional representations of the group SL(2, C) is extended to infinite‐dimensional representations. As an infinite‐dimensional representation, we use the principal series of representations realized by means of the special unitary group SU₂. As a result another form of the principal series of representations of SL(2, C) is obtained which describes the transformation law of an infinite set of numbers under the group transformation in a way which is very similar, but as a generalization, to the way spinors appear in the finite‐dimensional case.