Tensor Potential Description of Matter and Space, II Semi-guage and the Law of Conservation

Considered a unified field theory approach describing matter and space (metric tensor) by means of a 3-index tensor $P_{jk}^i$. It is shown that if the Lagrangian has partial U(1) gauge (semi-gauge) of the type $P^{i}{jk}->P^{i}{jk}+a \delta{^i_j} \phi{{,k}}+b \delta{^i_k} \phi{{,j}}+cg_{jk}g^{mi} \phi{_{,m}}$ where a,b,c are constants, then the Euler equations of motion contain the covariant low of conservation in the form $J_{;k}^k=0$.