A new scheme for color confinement due to violation of the non-Abelian Bianchi identities

A new scheme for color confinement in QCD due to violation of the non-Abelian Bianchi identities is discussed. The violation of the non-Abelian Bianchi identities (VNABI) $J_{\mu}$ is equal to Abelian-like monopole currents $k_{\mu}$ defined by the violation of the Abelian-like Bianchi identities. Although VNABI is an adjoint operator satisfying the covariant conservation rule $D_{\mu}J_{\mu}=0$, it gives us, at the same time, the Abelian-like conservation rule $\partial_{\mu}J_{\mu}=0$. The Abelian-like conservation rule $\partial_{\mu}J_{\mu}=0$ is also gauge-covariant. There are $N^2-1$ conserved magnetic charges in the case of color $SU(N)$. The charge of each component of VNABI is quantized \`{a} la Dirac. VNABI satisfying the Dirac quantization condition could be defined on lattice as lattice Abelian-like monopole currents without any gauge-fixing. Previous studies of the Abelian-like monopoles $k_{\mu}$ on lattice show that non-Abelian color confinement could be understood by the Abelian-like dual Meissner effect due to condensation of VNABI.