Reduction of the Poincaré Group with Respect to the Lorentz Group

Abstract

The representations of the Poincaré Group for spinless particles, reduced with respect to the Lorentz subgroup, are investigated. They involve the principal series of representations of SL(2, C) and use is made of a basis, introduced by Gel'fand in which the states are labeled by a complex number z. The transformation matrices relating to the Wigner basis are derived. The matrix elements of the momentum operators are obtained. The general form of the S matrix in the new basis is discussed. This basis may be relevant for a field theoretical description of the Veneziano model.