COMPLEX LANGEVIN FOR SEMISIMPLE COMPACT CONNECTED LIE-GROUPS AND U(1)

Several problems in quantum field theory like QCD at high densities le ad to complex-valued actions S with S : G --> C, where G is some group . Under the assumption that the complex Langevin process converges to a weakly stationary process we discuss the conditions under which it c orrectly simulates expectation values defined by complex weights. For technical reasons the discussion is restricted to (ill) and semisimple compact connected Lie groups like SU(n).