  Making the Lorentzian path integral for quantum gravity well-defined and
computable has been a long standing challenge. In this work we adopt the
recently proposed effective spin foam models to the Lorentzian case. This
defines a path integral over discrete Lorentzian quantum geometric
configurations, which include metric and torsion degrees of freedom. The
torsion degrees of freedom arise due to an anomaly, which is parametrized by
the Barbero--Immirzi parameter. Requiring a semi-classical regime constrains
this parameter, but the precise bound has to be determined by probing the
dynamics. The effective models provide the computationally most efficient spin
foam models yet, which allows us to perform first tests for determining the
semi-classical regime. This includes explorations specific to the Lorentzian
case, e.g. investigating quantum geometries with null lengths and null areas as
well as geometries that describe a change of spatial topology.
