Two-spinor description of massive particles and relativistic spin projection operators

摘要

On the basis of the Wigner unitary representations of the covering groupISL(2,C) of the Poincar\'{e} group, we obtain spin-tensor wave functions offree massive particles with arbitrary spin. The wave functions automaticallysatisfy the Dirac-Pauli-Fierz equations. In the framework of the two-spinorformalism we construct spin-vectors of polarizations and obtain conditions thatfix the corresponding relativistic spin projection operators (Behrends-Fronsdalprojection operators). With the help of these conditions we find explicitexpressions for relativistic spin projection operators for integer spins(Behrends-Fronsdal projection operators) and then find relativistic spinprojection operators for half integer spins. These projection operatorsdetermine the nominators in the propagators of fields of relativisticparticles. We deduce generalizations of the Behrends-Fronsdal projectionoperators for arbitrary space-time dimensions D>2.