Discrete Spacetime Models and Phenomenology  

In General > s.a. 3D quantum gravity; canonical quantum gravity; causal sets; Discrete Models [matter]; physics [ultimate theory proposals].
* Models: One possible way to group them into different types is:
- Combinatorial, non-topological versions, such as posets or graphs;
- Topological versions, such as simplicial or cell complexes;
- Piecewise-flat versions, such as Regge calculus, dynamical triangulations or twisted geometries;
To establish a connection with continuum geometry, each proposal of one of the above types seems to need the ones below as an intermediate step.
@ Spin networks and lqg: in Penrose 66, pr(66), in(70), in(71), in(72), in(79); Hasslacher & Perry PLB(81); Moussouris PhD(83); Kauffman IJMPA(90); LaFave gq/93; Zapata GRG(98)gq/97; Dupuis et al Sigma(12)-a1204 [rev]; Haggard et al PRD(13)-a1211 [twisted geometry, spin connection]; > s.a. spin-foam models.
@ Graphs / network models: Dadic & Pisk IJTP(79); Antonsen PhD(92), IJTP(94); Requardt ht/96, ht/96, ht/96-in [random graphs], JPA(98)ht, gq/99, CQG(00)gq/99, Requardt & Roy CQG(01)gq/00 [and random metric space]; Requardt gq/03; Markopoulou & Smolin PRD(04)gq/03; Konopka et al ht/06 [complete lattice, phase transition]; Efremov et al a0706 [BF theory on graph cobordisms]; Kan PTPS-a0712 [and cosmology]; Wall CQG(13)-a1201 [discrete causal dynamics]; Baird JGP(13); Hossenfelder CQG(15)-a1504 [no-go theorem for Poincaré-invariant networks]; Trugenberger PRE(15)-a1507 [and phase transition]; Bianconi & Rahmede SciRep(15)-a1506 [Complex Quantum Network Manifolds], PRE(16)-a1511 [network geometry with flavor, NGF]; Lombard a1602 [Metropolis network evolution simulations and emergent properties]; Trugenberger JHEP-a1610; Vanchurin a1706 [information flow graph].
@ Quantum graphity: Konopka et al ht/06 [proposal]; Konopka et al PRD(08)-a0801 [locality]; Konopka PRD(08)-a0805 [statistical mechanics, role of matter]; Hamma et al PRD(10) [entanglement of matter and geometry]; Caravelli & Markopoulou PRD(11)-a1008 [low-temperature properties]; Hamma & Markopoulou NJP(11)-a1011 [rev]; Caravelli a1110-proc; Caravelli & Markopoulou PRD(12)-a1201 [model of quantum foam]; Markopoulou LNCS(12)-a1201 [and quantum computation]; Quach et al PRD(12)-a1203 [formation of metastable defects at domain boundaries]; Wilkinson & Greentree PRD(14)-a1409 [energetics], PRD(15)-a1506 [hypervalence term in the Hamiltonian]; Requardt & Rastgoo JCA-a1501 [compared to dynamic cellular network approach]; > s.a. graphs in physics [graph evolution models].
@ Cellular automaton: Feynman; Finkelstein PR(69); 't Hooft NPB(90), et al NPB(92), gq/93; Requardt ht/95 [varying connections]; Zizzi gq/01-conf, gq/01, in(04)gq/03 [computational network]; Eakins & Jaroszkiewicz gq/03.
@ Fuzzy: Francis phy/99-wd, phy/99 [and particles]; Zizzi MPLA(05)gq/04-in [N-qubits on quantum space].
@ Other models: Noyes 01; Galiautdinov PhD-IJTP(02)ht [and spin-1/2 particles]; Abramsky in(05)-a1111 [topological universe of finitary sets]; Buniy et al PLB(05)ht [and discrete Hilbert space]; Tanaka FPL(06)ht/05 [Buniy-Hsu-Zee model and Yang's quantized spacetime algebra]; Zachos IJMPA(80)-a0710 [umbral deformation]; Deveaux & Fernández JSP(10)-a1002 [partially ordered chains]; Finster & Grotz ATMP(12)-a1107, Farrelly & Short PRA(14)-a1303 [causal fermion system], PRA(14)-a1312 [relativistic dynamics from particle in a discrete spacetime]; Cirilo-Lombardo & Prudencio IJGMP(14)-a1309 [supergeometry]; Ariwahjoedi et al a1607 [simplices]; > s.a. bose-einstein condensates; non-commutative geometry [including Snyder's proposal]; quantum spacetime models [categorical].
> Related concepts: see approaches to quantum gravity; discretized gravity; gravitational thermodynamics ["atoms of spacetime"]; renormalization.

Particles and Fields > s.a. diffusion; Discretization; graphs in physics; green functions; laplace operator.
@ General references: Dimakis et al JMP(95)ht/94 [fields]; Bojowald & Date CQG(04)gq/03 [consistency conditions on differential equations]; Bastin & Kilmister 09; Elze JPCS(09)-a0906; Weinstein a1101 [fixed number of degrees of freedom per co-moving volume, cosmology and variation of constants]; Sochichiu TMP(15)-a1403 [networks of fermionic states]; Canarutto a1404-FQXi.
@ Quantum field theory: Yamamoto PRD(85) [bosons and fermions]; Finster ATMP(07)mp/06, JPCS(07)ht/06, in(09)-a0712 [fermions]; Sverdlov a1108; Farrelly & Short PRA(14)-a1303 [fermions]; Berger & Yamatsu PRD(13); Kar et al MPLA(13)-a1305.
> Theories in discrete settings: see dirac fields; electromagnetism in curved spacetime; higher-dimensional gravity [discrete extra dimensions]; modified quantum field theories; path-integral quantum theory; quantum particles; wave equations.

Consequences / Phenomenology > s.a. quantum-gravity phenomenology; singularities; entropy bounds; ultra-high-energy cosmic rays.
@ Observability: Amelino-Camelia CzJP(98)gq-proc [discrete lengths and areas]; Rivero gq/06 [consequences]; Dreyer a0805 [cosmological perturbation spectrum]; Dreyer a1307 [cmb spectrum]; Brun & Mlodinow a1802 [matter interferometry].
@ Compatible with Lorentz symmetry: Rovelli & Speziale PRD(03)gq/02; Dowker et al MPLA(04)gq/03 [massive-particle diffusion on causal set background]; Livine & Oriti JHEP(04)gq [toy model + DSR quantum geometry]; Bombelli et al MPLA(09)gq/06, comment Kent a1803 [no breaking in random sprinklings]; Bonder a0801-conf [model, and Newtonian limit]; Burton a0912; Bonder & Sudarsky AIP(10)-a1003 [model and experimental setup]; Aguilar et al PRD(13)-a1210 [phenomenological signatures]; Jizba & Scardigli EPJC(13)-a1301, FP(14) [emergence of various symmetries at larger scales].
@ Lorentz symmetry, other: Sidharth IJTP(04); Vergeles NPB(06)ht/05; Henson gq/06; Hossenfelder CQG(15)-a1504 [no-go theorem]; > s.a. lorentz symmetry [emergence] and modifications.
@ Continuum limit: Ling MPLA(05)gq/03 [and singularities]; Requardt IJGMP(06)mp/05 [and distance between metric spaces]; > s.a. canonical quantum gravity [discreteness corrections].
@ Related topics: Badiali JPA(05) [and statistical thermodynamics]; Bachmat gq/07 [applications, ?]; Gao IJTP(10)-a1001 [and superposition of spacetimes]; Kauffman a1109 [discrete measurements and derivatives, non-commutativity and the imaginary unit]; Chamseddine a1606-proc [non-commutative space and grand unified models].

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