where n ^ ^ = ω ω → → / | ω ω → → | and f 1 , 2 ( k , k → → ⋅ ⋅ n ^ ^ ) are functions depending, in addition to k , on the scalar product k → → ⋅ ⋅ n ^ ^ . The variables k , k → → ⋅ ⋅ n ^ ^ are invariant not only under rotations of the vectors k → → , n ^ ^ but also under rotations and the Lorentz transformations of initial four-vectors k , ω ω . The second contribution ∝ ∝ Y l m ( n ^ ^ ) means that the operator of the total angular momentum in explicitly covariant light-front dynamics obtains an additional term: J → → = − − i [ k → → × × ∂ ∂ k → → ] − − i [ n ^ ^ × × ∂ ∂ n ^ ^ ] . For non-zero spin particles this operator obtains the contribution of the spin operators: