Four-dimensional spinfoam quantum gravity with a cosmological constant: Finiteness and semiclassical limit

We present an improved formulation of 4-dimensional Lorentzian spinfoam quantum gravity with a cosmological constant. The construction amplitudes uses the state-integral model $\mathrm{PSL}(2,\mathbb{C})$ Chern-Simons theory and implementation simplicity constraint. has two key features: (1) are all finite, (2) suitable boundary data, semiclassical asymptotics vertex amplitude oscillatory terms, phase plus or minus Regge action constant for curvature 4-simplex.