Abstract
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 Poincaré 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.
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ArXiv ePrint: 1403.7345
Work supported by the Research and Education Board at the University of Boras. (Anders K.H. Bengtsson)
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Bengtsson, A.K.H. A Riccati type PDE for light-front higher helicity vertices. J. High Energ. Phys. 2014, 105 (2014). https://doi.org/10.1007/JHEP09(2014)105
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DOI: https://doi.org/10.1007/JHEP09(2014)105