Path integral representation of spin foam models of 4d gravity
arXiv:0806.4640 · doi:10.1088/0264-9381/25/24/245010
Abstract
We give a unified description of all recent spin foam models introduced by Engle, Livine, Pereira and Rovelli (ELPR) and by Freidel and Krasnov (FK). We show that the FK models are, for all values of the Immirzi parameter, equivalent to path integrals of a discrete theory and we provide an explicit formula for the associated actions. We discuss the relation between the FK and ELPR models and also study the corresponding boundary states. For general Immirzi parameter, these are given by Alexandrov's and Livine's SO(4) projected states. For 0 <= gamma < 1, the states can be restricted to SU(2) spin networks.
29 pages, 6 figures
References in corpus (6)
- LQG vertex with finite Immirzi parameter
- A new spinfoam vertex for quantum gravity
- The loop-quantum-gravity vertex-amplitude
- Flipped spinfoam vertex and loop gravity
- A "general boundary" formulation for quantum mechanics and quantum gravity
- Coherent states, constraint classes, and area operators in the new spin-foam models