Infinite-dimensional representations of the Lorentz group: Complementary series of representations

The method used by Carmeli to obtain another form for the principal series of representations of the group SL(2, C) is extended to the complementary series of representations of that group. As a result, a new form for the complementary series of representations of SL(2, C) is obtained which describes the transformation law of an infinite set of numbers under the group translation in a way which is very similar, but as a generalization, to the way spinors appear in the finite-dimensional case.