  A general multi-orbital Hubbard model, which includes on-site inter-orbital
electron hoppings, is introduced and studied. It is shown that the on-site
inter-orbital single electron hopping is one of the most basic interactions.
Two electron spin-flip and pair-hoppings are shown to be correlation effects of
higher order than the on-site inter-orbital single hopping. It is shown how the
double and higher hopping interactions can be well-defined for arbitrary
systems. The two-orbital Hubbard model is studied numerically to demonstrate
the influence of the single electron hopping effect, leading to a change of the
shape of the bands and a shrinking of the difference between the two bands.
Inclusion of the on-site inter-orbital hopping suppresses the so-called
orbital-selective Mott transition.

Strongly Correlated Electrons;Superconductivity