Interaction of Non-Abelian Tensor Gauge Fields

Recently we introduced an extended vector bundle $X$ on which non-Abelian tensor gauge fields realize a connection. Our aim here is to introduce interaction of non-Abelian tensor gauge fields with fermions and bosons. We have found that there exist two series of gauge invariant forms describing this interaction. The linear sum of these forms comprises the general gauge invariant Lagrangian. Studying the corresponding Euler-Lagrange equations we found that a particular linear combination of these forms exhibits enhanced symmetry which guarantees the conservation of the corresponding high-rank currents. A possible mechanism of symmetry breaking and mass generation of tensor gauge bosons is suggested.