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spin foam wikipedia jump to content main menu main menu move to sidebar hide navigation main page contents current events random article about wikipedia contact us contribute help learn to edit community portal recent changes upload file special pages search search appearance donate create account log in personal tools donate create account log in contents move to sidebar hide top 1 in loop quantum gravity toggle in loop quantum gravity subsection 1 1 spin network 1 2 spacetime 2 definition 3 see also 4 references 5 external links toggle the table of contents spin foam 10 languages العربية català čeština deutsch italiano 日本語 한국어 português svenska 中文 edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia topological structure in loop quantum gravity beyond the standard model simulated large hadron collider cms particle detector data depicting a higgs boson produced by colliding protons decaying into hadron jets and electrons standard model evidence hierarchy problem dark matter dark energy quintessence phantom energy dark radiation dark photon cosmological constant problem strong cp problem neutrino oscillation theories brans dicke theory cosmic censorship hypothesis fifth force f theory theory of everything unified field theory grand unified theory technicolor kaluza klein theory 6d 2 0 superconformal field theory noncommutative quantum field theory quantum cosmology brane cosmology string theory superstring theory m theory mathematical universe hypothesis mirror matter randall sundrum model n 4 supersymmetric yang mills theory twistor string theory dark fluid doubly special relativity de sitter invariant special relativity causal fermion systems black hole thermodynamics unparticle physics graviphoton graviscalar graviton gravitino massive gravity gauge gravitation theory gauge theory gravity cpt symmetry supersymmetry mssm nmssm superstring theory m theory supergravity supersymmetry breaking extra dimensions large extra dimensions quantum gravity false vacuum string theory spin foam quantum foam quantum geometry loop quantum gravity quantum cosmology loop quantum cosmology causal dynamical triangulation causal fermion systems causal sets canonical quantum gravity semiclassical gravity superfluid vacuum theory experiments annie gran sasso ino lhc sno super k tevatron nova v t e in physics the topological structure of spinfoam or spin foam 1 consists of two dimensional faces representing a configuration required by functional integration to obtain a feynman s path integral description of quantum gravity these structures are employed in loop quantum gravity as a version of quantum foam in loop quantum gravity edit main article loop quantum gravity the covariant formulation of loop quantum gravity provides the best formulation of the dynamics of the theory of quantum gravity a quantum field theory where the invariance under diffeomorphisms of general relativity applies the resulting path integral represents a sum over all the possible configurations of spin foam how spin network edit main article spin network a spin network is a two dimensional graph together with labels on its vertices and edges which encode aspects of a spatial geometry a spin network is defined as a diagram like the feynman diagram which makes a basis of connections between the elements of a differentiable manifold for the hilbert spaces defined over them and for computations of amplitudes between two different hypersurfaces of the manifold any evolution of the spin network provides a spin foam over a manifold of one dimension higher than the dimensions of the corresponding spin network clarification needed a spin foam is analogous to quantum history why spacetime edit spin networks provide a language to describe the quantum geometry of space spin foam does the same job for spacetime spacetime can be defined as a superposition of spin foams which is a generalized feynman diagram where instead of a graph a higher dimensional complex is used in topology this sort of space is called a 2 complex a spin foam is a particular type of 2 complex with labels for vertices edges and faces the boundary of a spin foam is a spin network just as in the theory of manifolds where the boundary of an n manifold is an n 1 manifold in loop quantum gravity the present spin foam theory has been inspired by the ponzano regge model the idea was introduced by reisenberger and rovelli in 1997 2 and later developed into the barrett crane model the formulation that is used nowadays is commonly called eprl after the names of the authors of a series of seminal papers 3 but the theory has also seen fundamental contributions from the work of many others such as laurent freidel fk model and jerzy lewandowski kkl model definition edit the summary partition function for a spin foam model is z γ w γ j f i e f a f j f e a e j f i e v a v j f i e displaystyle z sum _ gamma w gamma left sum _ j_ f i_ e prod _ f a_ f j_ f prod _ e a_ e j_ f i_ e prod _ v a_ v j_ f i_ e right with a set of 2 complexes γ displaystyle gamma each consisting out of faces f displaystyle f edges e displaystyle e and vertices v displaystyle v associated to each 2 complex γ displaystyle gamma is a weight w γ displaystyle w gamma a set of irreducible representations j displaystyle j which label the faces and intertwiners i displaystyle i which label the edges a vertex amplitude a v j f i e displaystyle a_ v j_ f i_ e and an edge amplitude a e j f i e displaystyle a_ e j_ f i_ e a face amplitude a f j f displaystyle a_ f j_ f for which we almost always have a f j f dim j f displaystyle a_ f j_ f dim j_ f see also edit group field theory lorentz invariance in loop quantum gravity string net liquid references edit perez alejandro 2004 gr qc 0409061 introduction to loop quantum gravity and spin foams arxiv gr qc 0409061 reisenberger michael rovelli carlo 1997 sum over surfaces form of loop quantum gravity physical review d 56 6 3490 3508 arxiv gr qc 9612035 bibcode 1997phrvd 56 3490r doi 10 1103 physrevd 56 3490 engle jonathan pereira roberto rovelli carlo livine etera 2008 lqg vertex with finite immirzi parameter nuclear physics b 799 1 2 136 149 arxiv 0711 0146 bibcode 2008nuphb 799 136e doi 10 1016 j nuclphysb 2008 02 018 external links edit baez john c 1998 spin foam models classical and quantum gravity 15 7 1827 1858 arxiv gr qc 9709052 bibcode 1998cqgra 15 1827b doi 10 1088 0264 9381 15 7 004 s2cid 6449360 perez alejandro 2003 spin foam models for quantum gravity classical and quantum gravity 20 6 r43 r104 arxiv gr qc 0301113 doi 10 1088 0264 9381 20 6 202 s2cid 13891330 rovelli carlo 2011 zakopane lectures on loop gravity arxiv 1102 3660 gr qc v t e quantum gravity central concepts ads cft correspondence batalin vilkovisky formalism ca duality causal patch faddeev popov ghost gravitational anomaly graviton holographic principle ir uv mixing planck units quantum foam ryu takayanagi conjecture trans planckian problem weinberg witten theorem toy models 2 1d topological gravity cghs model jackiw teitelboim gravity liouville gravity rst model topological quantum field theory quantum field theory in curved spacetime bunch davies vacuum hawking radiation semiclassical gravity unruh effect black holes black hole complementarity black hole information paradox black hole thermodynamics bekenstein bound bousso s holographic bound cosmic censorship hypothesis er epr firewall physics gravitational singularity approaches string theory bosonic string theory m theory matrix theory physics supergravity superstring theory canonical quantum gravity loop quantum gravity wheeler dewitt equation euclidean quantum gravity hartle hawking proposal others causal dynamical triangulation causal sets dual graviton group field theory noncommutative geometry spin foam superfluid vacuum theory twistor theory applications quantum cosmology eternal inflation frw cft duality multiverse see also template quantum mechanics topics retrieved from https en wikipedia org w index php title spin_foam oldid 1350927211 categories theoretical physics loop quantum gravity hidden categories articles with short description short description is different from wikidata wikipedia articles needing clarification from may 2016 this page was last edited on 24 april 2026 at 21 39 utc page was rendered with parsoid text is available under the creative commons attribution sharealike 4 0 license additional terms may apply by using this site you agree to the terms of use and privacy policy wikipedia is a registered trademark of the wikimedia foundation inc a non profit organization privacy policy about wikipedia 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