On the Quantization of the Higher Spin Fields

In this article we quantize (massive) higher spin (1 ≤ j ≤ 2) fields by means of Dirac’s Constrained Hamilton procedure both in the situation were they are totally free and were they are coupled to (an) auxiliary field(s). A full constraint analysis and quantization is presented by determining and discussing all constraints and Lagrange multipliers and by giving all equal times (anti) commutation relations. Also we construct the relevant propagators. In the free case we obtain the well-known propagators and show that they are not covariant, which is also well known. In the coupled case we do obtain covariant propagators (in the spin-3/2 case this requires b = 0) and show that they have a smooth massless limit connecting perfectly to the massless case (with auxiliary fields). We notice that in our system of the spin-3/2 and spin-2 case the massive propagators coupled to conserved currents only have a smooth limit to the pure massless spin-propagator, when there are ghosts in the massive case.