  Recent observations have found that many $z\sim 6$ quasar fields lack
galaxies. This unexpected lack of galaxies may potentially be explained by
quasar radiation feedback. In this paper I present a suite of 3D radiative
transfer cosmological simulations of quasar fields. I find that quasar
radiation suppresses star formation in low mass galaxies, mainly by
photo-dissociating their molecular hydrogen. Photo-heating also plays a role,
but only after $\sim$100 Myr. However, galaxies which already have stellar mass
above $10^5 M_\odot$ when the quasar turns on will not be suppressed
significantly. Quasar radiative feedback suppresses the faint end of the galaxy
luminosity function (LF) within $1$ pMpc, but to a far lesser degree than the
field-to-field variation of the LF. My study also suggests that by using the
number of bright galaxies ($M_{1500}<-16$) around quasars, we can potentially
recover the underlying mass overdensity, which allows us to put reliable
constraints on quasar environments.
