A Riccati type PDE for light-front higher helicity vertices

This paper is based on a curious observation about an equation related to the tracelessness constraints of higher spin gauge fields. A similar equation also occurs in the theory of continuous spin representations of the Poincare group. Expressed in an oscillator basis for the higher spin fields, the equation becomes a non-linear partial differential operator of the Riccati type acting on the vertex functions. The consequences of the equation for the cubic vertex is investigated in the light-front formulation of higher spin theory. The vertex is fixed by the PDE up to a set of terms that can be considered as boundary data for the PDE. These terms can serve as off-shell quantum corrections. In order to set the present work in perspective, some comments and comparisons to recent research on higher spin interactions are made. A few particular cubic vertices are calculated explicitly and compared to similar results in the literature, in particular the interesting cases 2 - 3 - 3 and 3 - 2 - 2 involving spin 2 fields.