Discrete Spacetime Models and Phenomenology| 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 PRD(17)-a1602 [Metropolis network evolution simulations and emergent properties];
Trugenberger JHEP(17)-a1610;
Vanchurin FP(18)-a1706 [information flow graph];
Kelly & Trugenberger JPCS(19)-a1811 [random graphs];
Tee a1901 [quantum mesh];
Shoshany PRD(19)-a1904 [3D, discrete phase space].
@ 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];
Tee a1903 [quantum mesh dynamics];
> 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].
Wolfram model: Wolfram a2004;
Gorard a2004;
Rodríguez a2006;
> s.a. causal set dynamics.
@ 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];
De et al IJMPD(19)-a1903 [space-time-matter atoms];
Chirco et al PRD(19)-a1811 [tetrahedra, and maximum entropy principle];
Chirco & Kotecha LNCS(19)-a1906 [statistical framework];
> 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;
Dündar & Arık a1808 [?];
Rogers a1902-conf
[discrete vs continuum theories, history].
@ 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];
Hossenfelder CQG+(18) [violation of energy-momentum conservation];
Das et al a2006
[quantized lengths from GUP-modified quantum theory].
@ 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 CQG(18)-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];
Dowker & Sorkin CQG(20)-a1909.
@ 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 MPLA(16)-a1606-proc [non-commutative space and grand unified models];
> s.a. kinematics of special relativity [length contraction].
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 4 mar 2021