Non-Abelian tensor gauge fields and higher-spin extension of Standard Model

Abstract

We suggest an extension of the Yang-Mills theory which includes non-Abelian tensor gauge fields. The invariant Lagrangian is quadratic in the field strength tensors and describes interaction of charged tensor gauge bosons of arbitrary large integer spin $1,2,...$. Non-Abelian tensor gauge fields can be viewed as a unique gauge field with values in the infinite-dimensional current algebra associated with compact Lie group. The full Lagrangian exhibits also enhanced local gauge invariance with double number of gauge parameters which allows to eliminate all negative norm states of the nonsymmetric second-rank tensor gauge field, which describes therefore two polarizations of helicity-two massless charged tensor gauge boson and the helicity-zero boson. The geometrical interpretation of the enhanced gauge symmetry with double number of gauge parameters is not yet known. We suggest higher-spin extension of the electroweak theory and consider creation processes of new tensor gauge bosons.