Spin foam models for quantum gravity from lattice path integrals

Abstract

Spin foam models for quantum gravity are derived from lattice path integrals. The setting involves variables from both lattice BF theory and Regge calculus. The action consists in a Regge action, which depends on areas, dihedral angles and includes the Immirzi parameter. In addition, a measure is inserted to ensure a consistent gluing of simplices, so that the amplitude is dominated by configurations which satisfy the parallel transport relations. We explicitly compute the path integral as a sum over spin foams for a generic measure. The Freidel-Krasnov and Engle-Pereira-Rovelli models correspond to a special choice of gluing. In this case, the equations of motion describe genuine geometries, where the constraints of area-angle Regge calculus are satisfied. Furthermore, the Immirzi parameter drops out of the on-shell action, and stationarity with respect to area variations requires spacetime geometry to be flat.

19 pages, 1 figure

References in corpus (12)

• LQG vertex with finite Immirzi parameter
• A new spinfoam vertex for quantum gravity
• A New Spin Foam Model for 4d Gravity
• Flipped spinfoam vertex and loop gravity
• Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
• Area-angle variables for general relativity
• Quantum geometry from phase space reduction
• Group Integral Techniques for the Spinfoam Graviton Propagator
• Path integral representation of spin foam models of 4d gravity
• From lattice BF gauge theory to area-angle Regge calculus
• A Lagrangian approach to the Barrett-Crane spin foam model
• Semiclassical regime of Regge calculus and spin foams

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