Causal Sets  

In General > s.a. approaches to quantum gravity; posets; causal set dynamics and phenomenology.
* Causal set: A (locally) finite partially ordered set, in which the order is causally interpreted.
* Causal history: A causal set with additional structure, e.g., the SUq(2) intertwiners of spin networks, and/or other fields.
* Quantum causal history: A covariant functor from the poset of antichains to the category of Hilbert spaces.
@ Overviews: Sorkin in(90), in(91), in(95)gq, in(05)gq/03; Reid CJP(01)gq/99; in Markopoulou in(04)gq/02; Dowker in(05)gq, CP(06); Henson in(09)gq/06; Sorkin EO(06); Wallden JPCS(10)-a1001; Henson a1003-proc; Surya a1103-in.
@ Proposals: Kronheimer & Penrose PCPS(67); Myrheim CERN(78); 't Hooft in(78); Bombelli et al PRL(87); Bombelli PhD(87); Raptis gq/02 [algebraic version]; Sverdlov a0910 [reinterpretation]; Krugly a1004, a1008; Bolognesi a1004 [and the computational universe]; Dribus a1311.
@ Related topics: Ambjørn & Loll NPB(98)ht [2D]; Blute et al gq/01 [decoherent histories on causal sets]; Zohren PhD(08)-a0905 [and dynamical triangulations]; Sorkin JPCS(09)-a0910 [field of moving charge]; Knuth & Bahreyni a1005 [and special relativity]; Philpott PhD-a1009; Surya CQG(12)-a1110 [2D, phase transition]; Wüthrich JGPS(12)-a1207 [meaning]; Dowker GRG(13) [rev]; > s.a. causality [probabilistic]; entropy bound; information.

Kinematics > s.a. Alexandrov Sets; causal structure and spacetime; spin-foam models.
* Hauptvermutung: (Original version) If a causal set can be faithfully embedded in two Lorentzian manifolds (M, g) and (M', g'), then those two manifolds are close down to scales of the order of the embedding density.
* Coarse graining: A random coarse-graining procedure consists in starting with a causal set C and removing each point with probability p.
* Feature: Can implement the notion that spacetime topology may be scale-dependent; No known continuum approach can do this.
@ And posets: Low JMP(00); Droste JMP(05)gq [universal past-finite causal set]; Vatandoost & Bahrampour JMP(11) [and sphere orders].
@ Dimension: Meyer PhD(88), Ord(93); Reid PRD(03)gq/02; Eichhorn & Mizera CQG(14)-a1311 [spectral dimension]; Carlip CQG(15)-a1506, Belenchia et al PRD(16)-a1507 [reduction to spectral dimension = 2].
@ And continuum: Bombelli & Meyer PLA(89); Daughton CQG(98) [symmetric case]; Brightwell & Gregory PRL(91); Filk CQG(01)gq [time]; Requardt JMP(03)gq/01 [renormalization group]; Ilie et al CQG(06)gq/05 [longest paths and geodesics]; Henson CQG(06)gq [manifoldlike causal sets]; Brightwell et al CQG(08)-a0706, JPCS(09) [2D model]; Surya TCS(08)-a0712 [topology]; Rideout & Wallden CQG(09)-a0810, JPCS(09)-a0811 [lengths]; Benincasa & Dowker PRL(10)-a1001 [scalar curvature]; Krugly a1006 [unfaithful embeddings and matter]; Glaser & Surya PRD(13)-a1309 [proposed definition of locality]; Saravani & Aslanbeigi CQG(14)-a1403; Bolognesi & Lamb a1407; Gudder a1502 [and the emergence of 4D]; Gudder a1507 [c-causets and curvature].
@ Thickened spatial hypersurfaces: Major et al CQG(06)gq/05; Major et al JMP(07)gq/06; Major et al CQG(09)-a0902 [stable homology and manifoldlikeness]; Jubb a1611.
@ Specific types of metrics: He & Rideout CQG(09)-a0811 [Schwarzschild]; D'Ariano & Tosini a1008, SHPMP(13)-a1109, Cristina a1603 [Minkowski].
@ Related topics: Bleybel & Zaiour a1508 [results on temporal foliations].

Similar Proposals > s.a. models of spacetime; quantum spacetime and proposals [branching spacetime].
@ Quantum sets, causal nets: Finkelstein PR(69), PRD(72), PRD(72), PRD(74), IJTP(88), IJTP(89), IJTP(89), et al PRD(74), CQG(97)qp/96, qp/96; Finkelstein & Gibbs IJTP(93) [and groups]; Selesnick JMP(94) [Dirac fields], JMP(95) [gauge fields]; Hitchcock qp/00; Mallios & Raptis IJTP(01)gq [sheaves], IJTP(03)gq/02; Dukovski PRD(13); > s.a. observable algebras.
@ Causal histories: Markopoulou CMP(00)gq/98, CQG(00)ht/99, NPPS(00)ht/99; Hawkins et al CQG(03)ht; Markopoulou in(09)ht/06; Livine & Terno PRD(07) [and information theory]; Knuth & Bahreyni JMP(14)-a1209; Schaden a1509 [null lattice]; Gudder a1603 [from a 4D module over the integers].
@ Covariant, or c-causal sets: Gudder a1311, a1403; Gudder a1507 [inflation, multiverse, Hilbert space, Dirac operator].
@ Other proposals: Hemion FP(80), IJTP(88); Rylov JMP(90) [based on world function]; Raptis gq/99, gq/01 [based on topos]; Krugly IJTP(00) [with Grassmann variables], IJTP(02) [special types, and particles]; Zizzi gq/01/GRG-conf [qubit network]; Christensen & Crane JMP(05)gq/04 [causal sites]; Stavraki G&C(06) ["causal virtual algebraic structure"]; Brout gq/06-fs [with energy exchange and vacuum fluctuations]; Sen 10; Elze a1001-FQXi [dual partial orders]; Marin et al a1201 [gravity from order]; Mayburov PPN(12)-a1205 [fuzzy points/posets, and massive particle interactions]; Khoshbin-e-Khoshnazar G&C(13); Cortês & Smolin PRD(14)-a1307, PRD(14)-a1308, PRD(16)-a1407 [energetic causal sets]; Kalogeropoulos JPCS(14)-a1309 [asymptotic cones]; Stoica JoG(16)-a1504 [based on the horismos relation]; Bonezzi et al PRD(15)-a1505 [quantized causal structures from algebras of quantum observables].
> Related topics: see Causal Models; discrete geometries; generalized posets [non-commutative]; graph theory in physics.

Online Resources > see Sumati Surya's resource page; Wikipedia page.

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