Gauge invariant Lagrangian for non-Abelian tensor gauge fields of fourth rank

Abstract

Using generalized field strength tensors for non-Abelian tensor gauge fields one can explicitly construct all possible Lorentz invariant quadratic forms for rank-4 non-Abelian tensor gauge fields and demonstrate that there exist only two linear combinations of them which form a gauge invariant Lagrangian. Together with the previous construction of independent gauge invariant forms for rank-2 and rank-3 tensor gauge fields this construction proves the uniqueness of early proposed general Lagrangian up to rank-4 tensor fields. Expression for the coefficients of the general Lagrangian is presented in a compact form.