Regularization and finiteness of the Lorentzian LQG vertices

TL;DR

This paper provides an explicit form for Lorentzian vertices in loop quantum gravity, introduces a natural regularization, proves their finiteness, and offers a gauge-fixing interpretation.

Contribution

It presents a new explicit form for Lorentzian vertices, a natural regularization method, and proves their finiteness, advancing the mathematical foundation of loop quantum gravity.

Findings

Regularized vertices are finite.

Explicit form of Lorentzian vertices provided.

Gauge-fixing interpretation of regularization.

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.