SPIN ALGEBRAS AND POINCARE GROUP

The spin of an elementary particle is characterized in terms of the generators of the Poincaré group. A spin algebra, related to the canonical spin algebra, is constructed giving a preferred treatment to one particular space direction chosen to be that of the z-axis. The helicity operator is an element of the spin algebra, a second is defined so that it commutes with the generator of Lorentz transformations along the z-axis. A basis for a representation space is chosen in which the operators for space translations and this new spin algebra element are diagonal. The generators of the Poincaré group are represented in this basis. The basis is proven to be equivalent to the states defined by Kotański in terms of which the spin crossing matrices are diagonal. The phases for this basis are introduced wihtout using a singular rest state. The rest state in turn is defined from the general state by a unitary transformation. The problem of the azimuthal angles in scattering amplitudes is discussed and likewise the role that these angles play in the representation of the discrete elements of the Poincaré group. © 1969.