  We investigate the physical mechanisms that shape the luminosity function.
Beginning with the mass function of dark matter halos, we show how gas cooling,
photoionization, feedback, merging and thermal conduction affect the shape of
the luminosity function. We consider three processes whereby supernovae can
affect the forming galaxy: (1) reheating of disk gas to the halo temperature;
(2) expansion of the diffuse halo gas; (3) expulsion of cold disk gas from the
halo. While feedback of form (1) is able to flatten the faint end of the
luminosity function, this alone does not produce the sharp cut-off observed at
large luminosities. Feedback of form (2) is also unable to solve this problem.
The relative paucity of very bright galaxies can only be explained if cooling
in massive halos is strongly suppressed. Conduction is a promising mechanism,
but an uncomfortably high efficiency is required to suppress cooling to the
desired level. If, instead, superwinds are responsible for the lack of bright
galaxies, then the total energy budget required to obtain a good match to the
galaxy luminosity function greatly exceeds the energy available from supernova
explosions. The mechanism is only viable if the formation of central
supermassive black holes play a crucial role in limiting the amount of stars
that form in the host galaxy. (abridged)
