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 parameterized 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.

使量子引力的洛伦兹路径积分定义明确和可计算一直是一个长期存在的挑战。在这项工作中，我们将最近提出的有效自旋泡沫模型应用于洛伦兹案例。这定义了离散洛伦兹量子几何配置上的路径积分，其中包括度量和扭转自由度。扭转自由度由异常引起，由 Barbero-Immirzi 参数参数化。需要一个半经典体制限制了这个参数，但精确的界限必须通过探索动力学来确定。有效模型提供了计算上最有效的旋转泡沫模型，这使我们能够进行第一次测试以确定半经典状态。这包括特定于洛伦兹案例的探索，例如