Spin-Foam Models| Spin-Foam Models |
In General > s.a. 2D and 3D quantum gravity;
BF theory; lattice field theory [generalized gauge
theory] / 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; It 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 σ bounded by fixed
spin networks s and s',
W(s, s') = ∑spin foams bounded by s and s' measure(σ) Πvertices v Av(σ) ;
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 PhD(03)gq;
Pérez CQG(03)gq;
Miković ht/04-conf;
Pérez in(09)gq/06;
Alexandrov & Roche PRP(11)-a1009;
Bonzom PhD(10)-a1009;
Livine Hab(10)-a1101;
Banerjee et al Sigma(12)-a1109;
Pérez PiP-a1205,
LRR(13)-a1205;
Långvik a1303;
Engle ch(14)-a1303;
Rovelli & Vidotto 14.
@ General references: Freidel & Louapre NPB(03)gq/02 [diffeomorphisms];
Bojowald & Pérez GRG(10)gq/03 [anomalies and criteria];
Oeckl gq/03-proc [general boundary approach];
Bahr et al CQG(11)-a1010 [systematic approach, operator spin foams];
Rovelli & Smerlak CQG(12)-a1010 [combinatorial structure, summing = refining];
Kisielowski et al CQG(12)-a1107 [Feynman diagrammatic approach];
Wieland CQG(14)-a1301 [Hamiltonian formulation];
Bodendorfer & Neiman CQG(13)-a1303 [effective action, and trans-planckian regime];
Shirazi & Engle CQG(14)-a1308 [purely geometric path integral];
Smolin CQG(14) [general relativity as the equation of state];
Hnybida a1411-PhD [generating functionals];
Finocchiaro & Oriti a1812;
Belov a1905-PhD [geometry];
Asante et al PRL(20)-a2004 [effective models].
@ Simplicity constraints: Alexandrov PRD(08)-a0802,
Han & Thiemann CQG(13)-a1010 [and closure constraints];
Banburski & Chen PRD(16)-a1512 [simpler approach];
Han & Huang PRD(17)-a1702
[as surface defect in SL(2,C) Chern-Simons theory].
@ 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];
Bianchi et al PRD(10)-a1004 [holomorphic representation];
Han & Zhang CQG(12)-a1109 [on a 4D simplicial complex].
@ EPRL model: Perini a1211 [on arbitrary 2-complexes, holomorphic representation];
Han & Krajewski CQG(14)-a1304 [path integral representation];
Bahr & Belov PRD(18)-a1710 [volume simplicity constraint];
Donà et al PRL(19)-a1903 [numerical study].
@ Other Lorentzian: Baez CQG(98)gq/97;
De Pietri NPPS(97)gq,
gq/99-proc;
De Pietri & Freidel CQG(99)gq/98;
Freidel & Krasnov ATMP(98)ht;
Iwasaki gq/99;
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];
Pereira CQG(08)-a0710;
Barrett et al CQG(10)-a0907,
GRG(11) [graphical calculus, asymptotics];
Conrady & Hnybida CQG(10)-a1002;
Ding & Rovelli CQG(10)-a1006 [boundary Hilbert space and volume operator];
Han & Zhang CQG(13)-a1109 [on a 4D simplicial complex];
Bianchi & Ding PRD(12)-a1109 [propagator];
Perlov a1312;
Liu & Han a1810 [with timelike triangles];
Asante et al a2104 [effective models].
@ And causality: Gupta PRD(00)gq/99;
Oriti BJP(05)gq/04-proc,
PRL(05)gq/04 [Feynman propagator];
Immirzi a1610 [and the Regge action];
> s.a. causal sets [energetic causal sets].
@ And lqg: Pérez & Rovelli in(11)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];
Kamiński et al CQG(10)-a0909,
Ding et al PRD(11)-a1011 [arbitrary 2-cell spin-foams];
Marin a1003;
Rovelli & Speziale PRD(11)-a1012;
Bonzom PRD(11)-a1101 [and Hamiltonian constraint];
Dupuis PhD(10)-a1104 [and semiclassical limit];
Alexandrov et al Sigma(12)-a1112;
Speziale & Wieland PRD(12)-a1209 [and twistorial structure];
Engle CQG(13)-a1301 [without piecewise linearity];
Thiemann & Zipfel CQG(14)-a1307 [spin-foam projector];
Yang et al a2102;
> s.a. canonical quantum gravity [covariant].
@ Vertex amplitudes: Livine & Speziale PRD(07)-a0705,
EPL(08)-a0708;
Engle et al PRL(07)-a0705 [from relationship with lqg],
NPB(08)-a0708,
NPB(08)-a0711 [flipped, EPRL];
Freidel & Krasnov CQG(08)-a0708;
Engle & Pereira CQG(08)-a0710,
PRD(09)-a0805;
Conrady & Freidel CQG(08)-a0806 [path-integral representation];
Khavkine a0810-wd;
Bonzom et al CQG(10)-a0911 [recurrence relations];
Alexandrov PRD(10)-a1004 [and canonical quantization];
Engle PRD(13)-a1111;
Bianchi & Hellmann Sigma(13);
Engle & Zipfel PRD(16)-a1502 [Lorentzian];
Mielczarek a1810 [using quantum algorithms];
> s.a. geometry.
@ Face amplitudes: Bianchi et al CQG(10)-a1005;
Regoli PhD-a1104.
@ 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 CMP(10)-a0905 [holomorphic factorization];
Carfora et al JPCA(09)-a1001 [6j symbol];
Schliemann CQG(13)-a1307 [large-volume limit].
With Matter / For Other Theories
@ General references: Steinhaus PRD(15)-a1509 [coupled intertwiner dynamics toy model].
@ With Yang-Mills fields: Miković CQG(02)ht/01,
CQG(03)ht/02;
Speziale CQG(07)-a0706 [3D];
Alexander et al PLB(12)-a1105 [and matter, unification].
@ With fermions: Miković AIP(06)gq/05;
Fairbairn GRG(07)gq/06 [3D];
Dowdall & Fairbairn GRG(11)-a1003 [3D, observables];
Bianchi et al CQG(13)-a1012 [and Yang-Mills fields];
Han & Rovelli CQG(13)-a1101 [PCT symmetry, etc];
Crane a1105 [extension including the standard model].
@ With other matter: Smilga ht/04 [SO(3, 2)];
Fairbairn & Livine CQG(07)gq [3D];
Baccetti et al CQG(10)-a1004 [N = 1 supersymmetric];
Fani & Kaviani IJGMP(14)-a1102 [dimensional reduction and emergence of non-gravitational fields];
Kisielowski & Lewandowski CQG(19)-a1807 [scalar field].
@ And strings / M-theory: Grosse & Schlesinger PLB(02) [topological quantum field theories of 3-forms].
Related Topics and Other Variations
> s.a. acceleration [maximal]; Pachner
Moves; semiclassical quantum gravity.
@ Holonomy formulation: Magliaro & Perini IJMPD(12)-a1010;
Bahr JPCS(12)-a1112 [and coarse graining];
Bahr et al PRD(13)-a1208 [new holonomy formulation];
Dittrich et al CQG(13)-a1209;
Hellmann & Kamiński a1210 [on arbitrary triangulations, geometric asymptotics],
JHEP(13)-a1307.
@ Spin nets: Dittrich et al NJP(13)-a1306 [coarse graining and continuum phases];
Dittrich et al PRD(14)-a1312 [quantum group spin nets].
@ Classical limit: Magliaro & Perini EPL(11)-a1108;
Engle PLB(13)-a1201 [correct semiclassical limit];
Vojinović GRG(13)-a1307 [issue arising from vertex amplitudes];
Steinhaus & Thürigen a1803 [spectral dimension];
Donà et al CQG-a1909 [numerical].
@ Analytic continuation: Maran gq/05 [complex general relativity and various signatures];
Han & Liu a2104 [complex critical points].
@ Other variations: Zapata JMP(02) [continuum model];
Miković IJMPA(03)gq/02-conf [quantum field theory of spin networks];
García-Islas gq/04 [p-adic];
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];
Mamone & Rovelli CQG(09)-a0904 [second-order amplitudes];
Conrady CQG(10)-a1003 [with timelike surfaces];
Denicola et al CQG(10)-a1005 [with topological data];
Han JMP(11)-a1012,
Fairbairn & Meusburger JMP(12)-a1012,
PoS-a1112 [deformed versions];
Bonzom & Smerlak AHP(12)-a1103 [bubble divergences];
Magliaro & Perini CQG(11)-a1103 [curvature and discrete Einstein equations];
Bahr et al a1103 [with finite groups];
Magliaro & Perini IJMPD(13)-a1105 [and Regge gravity];
Perini JPCS(12)-a1110;
Dupuis et al a1201-proc [spinors and twistors];
Bonzom & Smerlak PRL(12)-a1201 [gauge symmetries and "cellular quantization"];
Puchta JPCS(12) [graphs and characterization of foams];
García-Islas IJMPA(12)-a1206 [measurement and information];
Immirzi CQG(14)-a1311 [spinor construction of amplitudes];
Perlov a1407;
Hnybida CQG(16)-a1508 [without spins, using generating functions instead of recoupling theory].
@ Coarse-graining: Markopoulou CQG(03)gq/02;
Dittrich et al NJP(12)-a1109;
Zapata JPCS(12)-a1203;
Dittrich & Steinhaus NJP(14)-a1311 [refining, entangling operators];
Dittrich et al PRD(16)-a1609 [intertwiners];
Delcamp & Dittrich a1612
[systematic scheme for 3D lattice gauge models based on decorated tensor networks];
Steinhaus a2007 [rev].
@ Renormalization:
Oeckl in(06)gq/04;
Livine & Oriti JHEP(07)gq/05;
Smerlak PhD(11)-a1201 [and divergences];
Bahr a1407 [background-independent];
Bahr & Steinhaus PRL(16)-a1605 [evidence for a phase transition],
PRD(17)-a1701 [hypercuboidal renormalization].
@ Perturbations: Baez gq/99;
Martins & Miković Sigma(11)-a0911.
@ Other types of spacetimes: Han & Zhang PRD(16)-a1606 [near a classical curvature singularity];
> s.a. 3D black holes.
@ Computational / numerical work: Khavkine CQG(09)-a0809;
Dittrich & Eckert JPCS(12)-a1111.
@ Other related topics: Bahr a1812 [non-convex 4D polytopes];
Ansel GRG(21) [open quantum system theory];
> s.a. black-hole entropy; dimensionality
of spacetime; FLRW models; graviton;
linearized quantum gravity [propagator]; quantum
cosmology.
Other State Sum Models
@ General features: Barrett gq/00-conf.
@ Categorical generalizations: Baratin & Wise AIP(09)-a0910 [based on 2-group representations];
Miković & Vojinović CQG(12)-a1110 [BFCG formulation];
Miković RVMP(13)-a1302 [spin-cube state sum models, representations of the Poincaré 2-group];
Miković & Vojinović JPCS(14)-a1512;
Miković et al CQG(18)-a1807 [BFCG formulation, Hamiltonian analysis].
@ Cube-based: Baratin et al NJP(12)-a0812 [cubations and Holst action];
Vojinović PRD(16)-a1506 [spincube models and causal dynamical triangulations].
@ Other models: Davids gq/01 [Lorentzian, SU(1,1)];
Pérez ATMP(01)gq/02 [Plebański SO(4) model];
Miković MPLA(05)gq-conf;
Bonzom PRD(09)-a0905 [from lattice path integrals];
Geiller & Noui CQG(12)-a1112 [3D Plebański SO(4) model].
> Quantum-gravity related:
see Barrett-Crane Model; Crane-Yetter Model;
Ponzano-Regge Model; Turaev-Viro Theory.
> In gauge theory and other theories:
> see path-integral quantization for gauge theories;
string theory.
> Online resources: see Dan
Christensen's page.
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 29 apr 2021