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.

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

References in corpus (8)

• LQG vertex with finite Immirzi parameter
• A new spinfoam vertex for quantum gravity
• A New Spin Foam Model for 4d Gravity
• The loop-quantum-gravity vertex-amplitude
• Flipped spinfoam vertex and loop gravity
• Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
• Simplicity and closure constraints in spin foam models of gravity
• Coherent states, constraint classes, and area operators in the new spin-foam models

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• How-To compute EPRL spin foam amplitudes
• Markov Chain Monte Carlo methods for graph refinement in Spinfoam Cosmology
• All 3-edge-connected relativistic BC and EPRL spin-networks are integrable
• Spinfoams and high performance computing
• Holonomy-flux spinfoam amplitude
• Spinfoams: Foundations
• Finiteness of spinfoam vertex amplitude with timelike polyhedra, and the full amplitude
• The new spin foam models and quantum gravity
• Geometry from local flatness in Lorentzian spin foam theories
• (2+1) Lorentzian quantum cosmology from spin-foams: opportunities and obstacles for semi-classicality