New approaches to finite density lattice field theory

Christof Gattringer, Graz

The fact that at non-zero chemical potential the action S becomes complex for many quantum field theories is a major obstacle for Monte Carlo simulations at finite density: The Boltzmann factorexp(-S) obtains a complex phase and cannot be interpreted as a probability weight. In recent years this so-called "complex action problem" was overcome for several systems by rewriting them to different degrees of freedom, so-called dual variables. These variables are closed loops for matter and surfaces for gauge fields. In term of the dual variables the partition sum has only real and positive contributions and Monte Carlo simulations are possible at arbitrary densities. We give an overview over these recent developments.