A theory is presented that relates the luminescence signal of a semiconduct
or to the current-density correlation function. It allows the calculation o
f the luminescence spectrum for nonthermal carrier distributions by means o
f solving the Bethe-Salpeter equation for the polarization. The present met
hod passes important consistency checks and overcomes some limitations and
shortcomings of previous approaches. A detailed comparison is made with pre
vious results and numerical examples are presented to demonstrate the usefu
lness of the present method.