Causal Sets| 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.
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.
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