4-dimensional Spin-foam Model with Quantum Lorentz Group

Abstract

We study the quantum group deformation of the Lorentzian EPRL spin-foam model. The construction uses the harmonic analysis on the quantum Lorentz group. We show that the quantum group spin-foam model so defined is free of the infra-red divergence, thus gives a finite partition function on a fixed triangulation. We expect this quantum group spin-foam model is a spin-foam quantization of discrete gravity with a cosmological constant.

23 pages, 3 figures, references added

References in corpus (11)

• 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
• Algebraic Quantum Gravity (AQG) I. Conceptual Setup
• Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
• Quantum gravity with a positive cosmological constant
• Generalized Spinfoams
• Physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory
• All 3-edge-connected relativistic BC and EPRL spin-networks are integrable
• Commuting Simplicity and Closure Constraints for 4D Spin Foam Models

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