Spin-Foam Models  

In General > s.a. 2D and 3D quantum gravity; lattice field theory [generalized gauge theory]; [loop quantum gravity and path-integral quantum gravity].
* Idea: The path integral counterpart of loop quantum gravity, spacetime versions of spin networks used either as tools to calculate amplitudes or considered as histories; Uses 2D complexes with faces labelled by representations of SU(2), edges labelled by intertwiners; States are combinations of spin networks, and amplitudes are often calculated as sums over spin foams bounded by fixed spin networks s and s',

W(s, s') = spinfoams bounded by s and s' measure() vertices v Av() ;

The difficult part is coming up with a good proposal for the vertex amplitudes Av.
@ Intros, reviews: Baez LNP(00)gq/99; Oriti RPP(01)gq; Livine PhD(03)gq; Oriti gq/03-PhD; Pérez CQG(03)gq; Mikovic ht/04-in; Pérez gq/06-in.
@ Euclidean: Reisenberger & Rovelli PRD(97)gq/96 [sum-over-surfaces lqg], gq/00, CQG(01)gq/00; Reisenberger gq/97; Iwasaki gq/00; Pérez NPB(01)gq/00 [finiteness].
@ Lorentzian / evolution: Baez CQG(98)gq/97; De Pietri gq/97-in, gq/99-in; De Pietri & Freidel CQG(99)gq/98; Freidel & Krasnov ATMP(98)ht; Iwasaki gq/99; Gupta PRD(00)gq/99 [causality]; Pérez & Rovelli PRD(01)gq/00, PRD(01)gq/00; Crane et al PRL(01)gq [finiteness of state sum]; Gambini & Pullin PRD(02)gq/01 [finite theory]; Maran gq/03, PRD(04)gq [and canonical quantum gravity]; Oriti gq/04-in, PRL(05)gq/04 [Feynman propagator, causality]; Pereira CQG(08)-a0710; Barrett et al a0907 [graphical calculus].
@ And lqg: Pérez & Rovelli gq/01 [transition amplitudes]; Arnsdorf CQG(02)gq/01; Livine CQG(02)gq, Livine & Oriti NPB(03)gq/02; Alesci et al PRD(08)-a0807 [and physical inner product]; Kaminski et al a0909 [arbitrary 2-cell spin-foams].
@ New proposals for vertex amplitudes: Livine & Speziale PRD(07)-a0705, a0708; Engle et al PRL(07)-a0705 [from relationship with lqg], NPB(08)-a0708, NPB(08)-a0711 [flipped]; Freidel & Krasnov CQG(08)-a0708; Engle & Pereira CQG(08)-a0710, PRD(09)-a0805; Conrady & Freidel CQG(08)-a0806 [path-integral representation]; Khavkine CQG(09)-a0809 [numerical evaluation]; Khavkine a0810; > s.a. geometry.
@ Quantum tetrahedra: Barbieri NPB(98)gq/97; Baez & Barrett ATMP(99)gq; Livine & Speziale CQG(08)-a0711 [boundary state]; Terno CQG(09)-a0808 [classical limit]; Freidel et al a0905.
@ Renormalization: Markopoulou CQG(03)gq/02 [coarse-graining]; Oeckl in(06)gq/04; Livine & Oriti JHEP(07)gq/05.
@ Coupled to Yang-Mills fields: Mikovic CQG(02)ht/01, CQG(03)ht/02; Speziale CQG(07)-a0706 [3D].
@ With other matter: Smilga ht/04 [SO(3,2)]; Mikovic AIP(06)gq/05 [fermions]; Fairbairn GRG(07)gq/06 [3D, fermions]; Fairbairn & Livine CQG(07)gq [3D].
@ Perturbations: Baez gq/99; Martins & Mikovic a0911.
@ And strings / M-theory: Grosse & Schlesinger PLB(02) [topological quantum field theories of 3-forms].
@ Related topics, variations: Zapata JMP(02) [continuum model]; Mikovic IJMPA(03)gq/02-in [quantum field theory of spin networks]; Freidel & Louapre NPB(03)gq/02 [diffeomorphisms]; Bojowald & Pérez gq/03 [anomalies and criteria]; Oeckl gq/03-in [general boundary approach]; García-Islas gq/04 [p-adic]; Maran gq/05 [complex general relativity and various signatures]; Baratin & Freidel CQG(07) [and 3D Feynman diagrams for quantum field theory], CQG(07)ht/06 [and 4D Feynman diagrams for quantum field theory]; Christensen et al PLB(09)-a0710 [area correlations]; Alexandrov PRD(08)-a0802 [simplicity and closure constraints]; García-Islas CQG(08)-a0809 [black-hole entropy]; Mamone & Rovelli a0904 [second-order amplitudes]; Bonzom et al a0911 [recurrence relations for vertices].
> Related topics: see 3D black holes; graviton; linearized quantum gravity [propagator]; semiclassical quantum gravity.

Ponzano-Regge Model > s.a. 3D gravity; SU(2).
* Idea: 3D spin coupling theory, giving a non-perturbative definition of the path integral for (Euclidean) 3D gravity.
@ General references: Ponzano & Regge in(68); Lewis PLB(83) [renormalizability]; Iwasaki gq/94, JMP(95)gq [in terms of surfaces]; O'Loughlin ATMP(02)gq/00 [boundary actions]; Barrett & Naish-Guzman CQG(09)-a0803.
@ Variations: Carfora et al PLB(93) [4D, and 12j symbols]; Carbone et al CMP(00); Freidel NPPS(00)gq/01 [Lorentzian]; Livine & Oeckl ATMP(03)ht/03 [supersymmetric].
@ Related topics: Barrett & Foxon CQG(94)gq/93 [semiclassical limit]; Petryk & Schleich PRD(03)gq/01 [geometric quantities]; Arcioni et al NPB(01)ht [and holography]; Freidel & Louapre CQG(04)ht [gauge fixing], gq/04 [and Chern-Simons theory]; Freidel & Livine CQG(06)ht/05 [effective field theory for particles]; Hackett & Speziale CQG(07)gq/06 [geometry and clasping rules]; Barrett & Naish-Guzman gq/06-in [and Reidemeister torsion]; Livine & Ryan CQG(09)-a0808 [B-observables]; Caravelli & Modesto a0905 [spectral dimension of spacetime].

Barrett-Crane Model > s.a. quantum regge calculus.
* Issue: 2007, There is a problem with the non-diagonal components of the graviton propagator [see 070918 ILQGS by J Engle].
@ General references: Barrett & Crane JMP(98)gq/97; Crane gq/97; Barrett ATMP(98)m.QA [evaluation]; Reisenberger JMP(99) [vertices]; Livine gq/01 [Immirzi parameter]; Pfeiffer CQG(02)gq/01 [Euclidean, dual variables]; Baez & Christensen CQG(02)gq/01 [positivity of amplitudes], et al CQG(02)gq [partition function]; Oriti PLB(02)gq [boundary terms]; Livine CQG(02)gq [and covariant lqg]; Lorente & Kramer gq/04-in [and SO(4) representations]; Lorente gq/04-in [Lorentz-invariant weight]; Maran JMP(06)gq/05 [derivation of intertwiner], gq/05-in [reality conditions]; Bonzom & Livine PRD(09)-a0812 [Lagrangian approach].
@ Lorentzian: Livine & Oriti NPB(03)gq/02, gq/03-in [causality]; Pfeiffer PRD(03)gq/02; Cherrington CQG(06)gq/05; Cherrington & Christensen CQG(06)gq/05 [positivity].
@ And BF theory: Oriti & Williams PRD(01)gq/00 [from discretized BF theory]; Livine & Oriti PRD(02)gq/01.
@ Effects: Alexander et al gq/03 [cosmology]; Girelli & Livine PRD(04)gq/03 [ > 0, speed quantization].
@ Deformed: Barrett & Crane CQG(00)gq/99 [Lorentzian]; Noui & Roche CQG(03)gq/02 [and > 0]; Khavkine & Christensen CQG(07)-a0704 [Riemannian, numerical, spin-spin correlation functions].
@ Variations: Pérez & Rovelli NPB(01)gq/00; Oriti & Pfeiffer PRD(02) [+ gauge fields]; Baez et al CQG(02), CQG(02) [numerical]; Maran gq/05 [SO(4,C) theory]; Alexandrov PRD(08)-a0705 [from covariant lqg]; Kramer & Lorente a0804, a0804.

Turaev-Viro Theory > s.a. models of topology change.
* Idea: 3D Riemannian quantum gravity with > 0; A spin coupling theory, quantum-group generalization of the Ponzano-Regge model, giving a non-perturbative definition of the path integral for 3D gravity; The Turaev-Viro state sum invariant is known to give the transition amplitude for the 3D BF theory with a cosmological constant, related to the its deformation parameter by = 1/2.
@ References: Turaev & Viro Top(92); Ionicioiu gq/96 [3-manifold partition function]; Girelli et al CQG(02)gq/01 [topological invariance]; García-Islas CQG(04)gq, Barrett et al JMP(07)m.QA/04 [observables].

Other State Sum Models in Quantum Gravity and Gauge Theory > s.a. pah-integral quantization for gauge theories; string theory.
* Crane-Yetter model: A 4D spin-coupling theory.
@ General features: Barrett gq/00-in.
@ Crane-Yetter model: Crane & Yetter gq/03; Barrett et al JMP(07)m.QA/04 [observables].
@ Other models: Davids gq/01 [Lorentzian, SU(1,1)]; Pérez ATMP(01)gq/02 [Plebanski SO(4) model]; Mikovic gq/05-in; Baratin et al a0812 [based on cubations and Holst action]; Bonzom PRD(09)-a0905 [from lattice path integrals]; Baratin & Wise a0910-in [based on 2-group representations].

Online Resources > see Dan Christensen's page.

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