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

Boris Hikin
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Abstract

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

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Boris Hikin. 2006-09-20. Tensor Potential Description of Matter and Space, II Semi-guage and the Law of Conservation. https://arxiv.org/abs/gr-qc/0609082

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