Effective action and semiclassical limit of spin foam models

Abstract

We define an effective action for spin foam models of quantum gravity by adapting the background field method from quantum field theory. We show that the Regge action is the leading term in the semi-classical expansion of the spin foam effective action if the vertex amplitude has the large-spin asymptotics which is proportional to an exponential function of the vertex Regge action. In the case of the known three-dimensional and four-dimensional spin foam models this amounts to modifying the vertex amplitude such that the exponential asymptotics is obtained. In particular, we show that the ELPR/FK model vertex amplitude can be modified such that the new model is finite and has the Einstein-Hilbert action as its classical limit. We also calculate the first-order and some of the second-order quantum corrections in the semi-classical expansion of the effective action.

Improved presentation, 2 references added. 15 pages, no figures

References in corpus (8)

• LQG vertex with finite Immirzi parameter
• The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex
• The Ponzano-Regge model
• 4-dimensional Spin-foam Model with Quantum Lorentz Group
• Face amplitude of spinfoam quantum gravity
• Emergence of gravity from spinfoams
• Semiclassical regime of Regge calculus and spin foams
• Errata to "Flat Spacetime Vacuum in Loop Quantum Gravity"

Cited by in corpus (18)

• The Spin Foam Approach to Quantum Gravity
• Lorentzian spinfoam propagator
• Quantum Cosmology: Effective Theory
• The twistorial structure of loop-gravity transition amplitudes
• Imaginary action, spinfoam asymptotics and the 'transplanckian' regime of loop quantum gravity
• A spin-foam vertex amplitude with the correct semiclassical limit
• Poincare 2-group and quantum gravity
• Covariant Loop Quantum Gravity, Low Energy Perturbation Theory, and Einstein Gravity with High Curvature UV Corrections
• Spin-cube Models of Quantum Gravity
• Solution to the Cosmological Constant Problem in a Regge Quantum Gravity Model
• Canonical formulation of Poincare BFCG theory and its quantization
• Hamiltonian analysis of the BFCG theory for the Poincare 2-group
• A finiteness bound for the EPRL/FK spin foam model
• Fermion spins in loop quantum gravity
• Effective action for EPRL/FK spin foam models
• Hamiltonian analysis of the BFCG formulation of General Relativity
• The 3BF theory as a TQFT
• Categorical generalization of spinfoam models