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

TL;DR

This paper proposes a unified field theory using a 3-index tensor to describe matter and space, demonstrating that a semi-gauge symmetry leads to a covariant conservation law within the Euler equations of motion.

Contribution

It introduces a semi-gauge invariance in a tensor-based unified field theory, linking gauge symmetry to conservation laws in matter-space interactions.

Findings

Semi-gauge symmetry induces covariant conservation law.

Unified description of matter and space via a 3-index tensor.

Euler equations reflect a covariant conservation law.

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 $P^{i}_{jk}->P^{i}_{jk}+a \delta{^i_j} \phi{_{,k}}+b \delta{^i_k} \phi{_{,j}}+cg_{jk}g^{mi} \phi{_{,m}}$ where a,b,c are constants, then the Euler equations of motion contain the covariant low of conservation in the form $J^{k}_{;k}=0$.