Spin Foam Quantization and Anomalies

Abstract

The most common spin foam models of gravity are widely believed to be discrete path integral quantizations of the Plebanski action. However, their derivation in present formulations is incomplete and lower dimensional simplex amplitudes are left open to choice. Since their large-spin behavior determines the convergence properties of the state-sum, this gap has to be closed before any reliable conclusion about finiteness can be reached. It is shown that these amplitudes are directly related to the path integral measure and can in principle be derived from it, requiring detailed knowledge of the constraint algebra and gauge fixing. In a related manner, minimal requirements of background independence provide non trivial restrictions on the form of an anomaly free measure. Many models in the literature do not satisfy these requirements. A simple model satisfying the above consistency requirements is presented which can be thought of as a spin foam quantization of the Husain--Kuchar model.

32 pages

References in corpus (5)

• Spin Foam Models for Quantum Gravity
• Three dimensional loop quantum gravity: physical scalar product and spin foam models
• Ponzano-Regge model revisited I: Gauge fixing, observables and interacting spinning particles
• Diffeomorphisms and spin foam models
• Hamiltonian Analysis of Plebanski Theory

Cited by in corpus (29)

• The Spin Foam Approach to Quantum Gravity
• Quantum cosmology: a review
• Phase space descriptions for simplicial 4d geometries
• Coarse graining methods for spin net and spin foam models
• Perfect discretization of reparametrization invariant path integrals
• Spin Foams and Canonical Quantization
• Holonomy Spin Foam Models: Definition and Coarse Graining
• Face amplitude of spinfoam quantum gravity
• Path integral measure and triangulation independence in discrete gravity
• Time evolution as refining, coarse graining and entangling
• Operator Spin Foam Models
• Coarse graining flow of spin foam intertwiners
• Quantum Cosmology: Effective Theory
• The twistorial structure of loop-gravity transition amplitudes
• $BF$ gravity
• Quantum group spin nets: refinement limit and relation to spin foams
• Critical Overview of Loops and Foams
• Discretization independence implies non-locality in 4D discrete quantum gravity
• Mathematical Structure of Loop Quantum Cosmology: Homogeneous Models
• Bubble divergences and gauge symmetries in spin foams
• The Holst Spin Foam Model via Cubulations
• Feynman diagrammatic approach to spin foams
• Towards computational insights into the large-scale structure of spin foams
• Loop quantization from a lattice gauge theory perspective
• One vertex spin-foams with the Dipole Cosmology boundary
• Coupled intertwiner dynamics: A toy model for coupling matter to spin foam models
• A path-integral approach to the problem of time
• Local spin foams
• Transition probability spaces in loop quantum gravity