We review the theory and applications of complex stochastic quantization to the quantum
many-body problem. Along the way, we present a brief overview of a number of ideas that …

The complex Langevin method is a promising approach to the complex-action problem
based on a fictitious time evolution of complexified dynamical variables under the influence …

These lecture notes contain an elementary introduction to lattice QCD at nonzero chemical
potential. Topics discussed include chemical potential in the continuum and on the lattice; …

We use the sign-reweighting method to simulate the QCD chiral transition at real baryon
densities on phenomenologically relevant lattices. This avoids the severe limitations of …

The complex Langevin method aims at performing path integral with a complex action
numerically based on complexification of the original real dynamical variables. One of the …

I will review the state of the art of the equation of state for strongly interacting matter from first
principles. I will discuss results at zero and finite chemical potential. For the latter, I will focus …

A bstract All approaches currently used to study finite baryon density lattice QCD suffer from
uncontrolled systematic uncertainties in addition to the well-known sign problem. We …

The pressure and energy density of the quark-gluon plasma at finite baryon chemical
potential are calculated using the complex Langevin equation. The stout smearing …

One reason for the well-known fact that the complex Langevin (CL) method sometimes fails
to converge or converges to the wrong limit has been identified long ago: it is insufficient …

In this review we present the current state-of-the-art on complex Langevin simulations and
their implications for the QCD phase diagram. After a short summary of the complex …