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A nonperturbative study of field theories with a complex action, such as QCDat finite baryon density, is difficult due to the sign problem. We show thatthe relativistic Bose gas at finite chemical potential has a sign and `SilverBlaze' problem, similar to QCD. We then apply stochastic quantization andcomplex Langevin dynamics to study this theory with nonperturbative latticesimulations. Independence of chemical potential at small and a transition to acondensed 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, wefind that it has no negative effect using this approach. This improves theprospects of applying stochastic quantization to QCD at nonzero density.

Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential