Spin foam models for quantum gravity

2003/01/31 by Alejandro Perez, Alejandro Pérez · 9 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Discretization #Epistemology #Field (mathematics) #Gauge (firearms) #Gauge theory #Geometry #Group field theory #Independence (probability theory) #Loop quantum gravity #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Perspective (graphical) #Physics #Pure mathematics #Quantum #Quantum gravity #Quantum mechanics #Simple (philosophy) #Spin (aerodynamics) #Spin foam #Theoretical physics #gr-qc #hep-th

paper · pdf · doi:10.1088/0264-9381/20/6/202

published as Class.Quant.Grav. 20 (2003) R43 · Topical review, to appear in CQG. Typos corrected and new references added

arxiv created 2003/02/14 · openalex publication_date 2003/02/21 · arxiv updated 2017/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this topical review, we review the present status of the spin foam formulation of non-perturbative (background-independent) quantum gravity. The topical review is divided into two parts. In the first part, we present a general introduction to the main ideas emphasizing their motivation from various perspectives. Riemannian three-dimensional gravity is used as a simple example to illustrate conceptual issues and the main goals of the approach. The main features of the various existing models for four-dimensional gravity are also presented here. We conclude with a discussion of important questions to be addressed in four dimensions (gauge invariance, discretization independence, etc). In the second part, we concentrate on the definition of the Barrett–Crane model. We present the main results obtained in this framework from a critical perspective. Finally, we review the combinatorial formulation of spin foam models based on the dual group field theory technology. We present the Barrett–Crane model in this framework and review the finiteness results obtained for both its Riemannian and its Lorentzian variants.

Citations

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• An algebraic approach to coarse graining
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• Immirzi parameter in the Barrett-Crane model?
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• Boundary terms in the Barrett–Crane spin foam model and consistent gluing
• Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity
• Nonperturbative summation over 3D discrete topologies
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• A generalized Hamiltonian constraint operator in loop quantum gravity and its simplest Euclidean matrix elements
• Loop space representation of quantum general relativity
• Spin foam models of matter coupled to gravity
• A Lorentzian signature model for quantum general relativity
• Spin foams as Feynman diagrams
• Real and complex connections for canonical gravity
• Worldsheet formulations of gauge theories and gravity
• New Variables for Classical and Quantum Gravity
• Loop Quantum Gravity
• Dual formulation of spin network evolution
• Recent Developments in Non-Perturbative Quantum Gravity
• Real Ashtekar variables for Lorentzian signature space-times
• Hilbert space structure of covariant loop quantum gravity
• Projective techniques and functional integration for gauge theories
• An efficient algorithm for the Riemannian 10 j symbols
• Hamiltonian formulation of Wilson's lattice gauge theories
• Spin foam model for Lorentzian general relativity
• Categorical Physics
• Topological Field Theory As The Key To Quantum Gravity
• A reformulation of the Ponzano-Regge quantum gravity model in terms of surfaces

Cited by

• AN INVITATION TO LOOP QUANTUM GRAVITY
• Bubble Divergences from Cellular Cohomology
• Classical general relativity as BF-Plebanski theory with linear constraints
• The physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory
• Cosmological constant from a deformation of the Wheeler–DeWitt equation
• Hamiltonian formulation of a simple theory of the teleparallel geometry
• Spin-foam model for gravity coupled to massless scalar field
• Spin Foam Models of Gravity and BF Theory as evolution of Spin Networks
• Commuting simplicity and closure constraints for 4D spin-foam models