  Using the Keldysh technique, we derive a set of quasiclassical equations for
Bloch electrons in noncentrosymmetric crystals upon excitation with
quasimonochromatic radiation in the presence of external electrical and
magnetic fields. These equations are the analog to the
semiconductor-Bloch-equations for the dynamics of electrons including the
photogalvanic effect (PGE) in particular the shift mechanism. The shift PGE was
recently identified as showing promise for the development of new photovoltaic
materials. In addition, our theory may be useful to investigate the interplay
between breaking time-reversal symmetry and topological properties as well as
the analysis of recent local excitation experiments in nanophotonics. Explicit
results for the photogalvanic tensors are presented for linear and circular
polarized light and a magnetic field. In addition, we disprove existing
statements that the shift-photogalvanic effect does not contribute to the
photo-Hall current.
