Weyl field strength symmetries for arbitrary helicity and gauge invariant Fierz-Pauli and Rarita-Schwinger wave equations

Abstract

The algebra of the restricted Lorentz group and the Weyl formulation of massless Poincare irreducible fields have been developed by primarily Lorentz-covariant Pauli matrix methods which facilitate the generation of both indexed Weyl spinor identities and Dirac identities. The results have been used to display a complex set of symmetries for the (anti)self-dual Weyl field strengths of arbitrary helicity j(>or=1). These symmetries and the requirement of Poincare irreducibility have then been used to give a direct and uniform determination of the forms of the gauge invariant (Lagrangian) free field wave equations for the Fierz-Pauli and Rarita-Schwinger potentials of spin 1, 3/2 and 2. The procedures set out indicate that it should be possible to establish the gauge invariant Lagrangian free field wave equations of arbitrary helicity in a uniform and direct manner from the corresponding much simpler equations governing the field strengths in unmixed spin representations.