Massive Dirac field in 3D and induced equations for higher spin fields

Abstract

On the example of the free massive Dirac in flat three-dimensional spacetime, we show how the linearised equations of motion for higher spin fields can be obtained from the induced action by coupling higher spin fields to conserved currents. The result is important because a classical analysis leads to many different formulations of free higher spin equations, and not all of them are expected to be a good starting point for introduction of interactions. Our result breaks the degeneracy. We express the results by using a metric-like description for higher spin fields, in which the equations of motion can be elegantly written in generic form that is valid for all spins.