On the Quantization of the Higher Spin Fields

TL;DR

This paper develops a Hamiltonian quantization method for massive higher spin fields (spin 1 to 2), analyzing constraints, propagators, and their covariant properties, including the massless limit and ghost issues.

Contribution

It provides a comprehensive Hamiltonian quantization framework for higher spin fields with explicit constraint analysis and covariant propagators, including the effects of auxiliary fields and massless limits.

Findings

Free propagators are non-covariant, as expected.

Coupled propagators can be made covariant with specific conditions.

Massless limits are smooth only when ghosts are present in the massive case.

Abstract

In this article we quantize (massive) higher spin ($1\leq j\leq2$) 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.