Abstract
Using generalized field strength tensors we constructed all possible Lorentz invariant quadratic forms for the rank-4 non-Abelian tensor gauge field and demonstrated that there exist only two linearly independent combinations of them which are gauge invariant. Together with the previous result for the rank-2 and rank-3 tensor gauge fields this construction proves the uniqueness of early proposed Lagrangian up to rank-4 tensor fields.
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