High spin, high derivatives

Abstract

This work is dedicated to honour the memory of Victor Manuel Villanueva Sandoval. One of the academic interests shared with Victor was the disturbing fact that despite many years of work of the most talented people, there is no consistent quantum field theory formulation for interacting high spin particles. We propose here a formalism for the description of high spin particles by directly generalizing the structure of Dirac theory for spin 1/2 to the (j, 0) ⊕ (0, j) representation. We find that this generalization leads naturally to a formalism of order 2j in the derivatives of the field. For j > 1, we conjecture that this construction evades the linear instabilities of the Ostrogradski theorem for theories with higher than two time derivatives due to the constriction introduced by the projection onto subspaces of well defined parity.