Regularization and finiteness of the Lorentzian LQG vertices
  We give an explicit form for the Lorentzian vertices recently introduced for possibly defining the dynamics of loop quantum gravity. As a result of so doing, a natural regularization of the vertices is suggested. The regularized vertices are then proven to be finite. An interpretation of the regularization in terms of a gauge-fixing is also given. 
Jonathan Engle and Roberto Pereira