POINT PARTICLE IN GENERAL BACKGROUND FIELDS AND FREE GAUGE THEORIES OF TRACELESS SYMMETRIC TENSORS

Abstract

Point particle may interact with traceless symmetric tensors of arbitrary rank. Free gauge theories of traceless symmetric tensors are constructed, which provides a possibility for a new type of interactions, when particles exchange by those gauge fields. The gauge theories are parametrized by the particle's mass m and otherwise are unique for each rank s. For m=0, they are local gauge models with actions of 2s th order in derivatives, known in d=4 as "pure spin," or "conformal higher spin" actions by Fradkin and Tseytlin. For m≠0, each rank-s model undergoes a unique nonlocal deformation which entangles fields of all ranks, starting from s. There exists a nonlocal transform which maps m≠0 theories onto m=0 ones, however, this map degenerates at some m≠0 fields whose polarizations are determined by zeros of Bessel functions. Conformal covariance properties of the m=0 models are analyzed, the space of gauge fields is shown to admit an action of an infinite-dimensional "conformal higher spin" Lie algebra which leaves gauge transformations intact.