  A nonperturbative study of field theories with a complex action, such as QCD
at finite baryon density, is difficult due to the sign problem. We show that
the relativistic Bose gas at finite chemical potential has a sign and `Silver
Blaze' problem, similar to QCD. We then apply stochastic quantization and
complex Langevin dynamics to study this theory with nonperturbative lattice
simulations. Independence of chemical potential at small and a transition to a
condensed phase at large chemical potential are found. Lattices of size N^4,
with N=4,6,8,10, are used. We show that the sign problem is severe, however, we
find that it has no negative effect using this approach. This improves the
prospects of applying stochastic quantization to QCD at nonzero density.
