  We apply a general method developed recently for the derivation of the
diagonal representation of an arbitrary matrix valued quantum Hamiltonian to
the particular case of Bloch electrons in an external electromagnetic field. We
find the diagonal representation as a series expansion to the second order in
$\hbar .$ This result is the basis for the determination of the effective
in-band Hamiltonian of interacting Bloch electrons living in different energy
bands. Indeed, the description of effects such as magnetic moment-moment
interactions mediated by the magnetic part of the full electromagnetic
interaction requires a computation to second order in $\hbar $. It is found
that the electronic current is made of two contributions: the first one comes
from the velocity and the second one is a magnetic moment current similar to
the spin current for Dirac particles. This last contribution is responsible for
the interaction between magnetic moments similarly to the spin-spin interaction
in the Breit Hamiltonian for Dirac electrons in interaction.
