Lagrange multiplier formalism for a spin-3/2 field

Abstract

It is proposed that the method of keeping the subsidiary conditions separate from the equations of motion in a consistent way by means of a Lagrange multiplier may be the solution to the various pathologies afflicting high-spin field theories. The distinct features of this approach are discussed with reference to a massive spin-³/₂ field. It is shown that in this formulation there is no causality violation for propagation in an external field and the energy spectrum in a homogeneous magnetic field is real. Quantization is carried out in a Hilbert space with indefinite metric. For minimal electromagnetic interaction a unitary S matrix is constructed by introducing a fictitious particle and an additional vertex.