Regularization and finiteness of the Lorentzian LQG vertices

Abstract

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.Comment: 16 pages; Added an appendix presenting the gauge-fixing interpretation, added three references, and made some minor change