Causal Sets  

In General > s.a. approaches to quantum gravity \ causality in quantum theory.
* 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.
@ 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; Dowker GRG(13); focus issue CQG(18); Eichhorn JPCS(19)-a1902 [roadmap]; Surya LRR(19)-a1903.
@ 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, Dribus 17.
@ Numerical simulations: Henson et al a1504 [MCMC algorithm and asymptotic regime]; Cunningham & Krioukov CPC(18)-a1709 [code for generation and study of causal sets]; Cunningham a1805-PhD [high-performance algorithms]; > s.a. posets.
@ Related topics: Blute et al gq/01 [decoherent histories on causal sets]; Sorkin JPCS(09)-a0910 [field of moving charge]; Knuth & Bahreyni a1005 [and special relativity]; Philpott PhD-a1009; Wüthrich JGPS(12)-a1207 [meaning]; Brightwell & Luczak a1510 [mathematical aspects]; Pinzani & Gogioso a2003 [superpositions]; Sverdlov a2006 [continuous measurement, infinite causal set]; Wüthrich & Huggett a2009-ch [spacetime emergence]; > s.a. causality [probabilistic]; entropy bound; gravity and information.

blue bullet Specific aspects: see causal set kinematics [including phase transitions]; dynamics and phenomenology [including matter description]; posets.

Similar Proposals > s.a. models of spacetime; quantum spacetime and proposals [branching spacetime].
* Quantum causal history: A covariant functor from the poset of antichains to the category of Hilbert spaces; Or, an extension of a causal set in which at each element of the causal set is assigned a Hilbert space of quantum states, and the local causal evolutions between events are modelled by competely positive and trace-preserving maps.
@ 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]; Guo JPA(20)-a1906 [tensor network representation]; > s.a. tensor networks.
@ Dynamical triangulations: Zohren PhD(08)-a0905; > s.a. causal dynamical triangulations.
@ Covariant, or c-causal sets: Gudder a1311, a1403; Gudder a1507 [inflation, multiverse, Hilbert space, Dirac operator].
@ Energetic causal sets: Cortês & Smolin PRD(14)-a1307, PRD(14)-a1308, PRD(16)-a1407; Cohen et al a1902 [retrocausality]; > s.a. hidden variables.
@ 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); 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]; Kissinger et al a1708 [and process theory]; Bayandin a2001 [causal discrete field theory].
> Related topics: see Causal Models; discrete spacetime models; generalized posets [non-commutative]; graph theory in physics.

Online Resources > see Wikipedia page.

main pageabbreviationsjournalscommentsother sitesacknowledgements
send feedback and suggestions to bombelli at – modified 11 may 2021