Infinite-dimensional representations of the Lorentz group

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.