  We show that a general principle of physical independence or physical
invariance of mathematical background manifold leads to a replacement of the
common derivative operators by the covariant co-derivative ones. This
replacement naturally induces a background matrix, by means of which we obtain
an effective Lagrangian for the minimal standard model with supplement terms
characterizing Lorentz invariance violation or anisotropy of space-time. We
construct a simple model of the background matrix and find that the strength of
Lorentz violation of proton in the photopion production is of the order
$10^{-23}$.
