Causal Set Dynamics and Phenomenology| Causal Set Dynamics and Phenomenology |
In General > s.a. causal sets.
* Idea: The formulation
of dynamics must ultimately be done in the context of a quantum theory,
the most promising approach being a sum-over-histories one, for example
with amplitudes of the type U(A, B) = ∑
paths exp{i S/\(\hbar\)}; Until a quantum
framework can be developed, classical models can provide useful insights.
@ References: Kastner in(16)-a1411 [and the transactional interpretation of quantum theory];
Wüthrich & Callender BJPS-a1502 [novel, global notion of becoming].
Sequential Growth Dynamics
* Idea: A classical
stochastic evolution scheme in which posets are sequentially grown, with
covariance and causality restrictions; Each new element is assigned a
probability of being related to each existing one; A special family of
probabilities is transitive percolation.
@ General references: Sorkin IJTP(97)gq,
IJTP(00)gq;
Rideout & Sorkin PRD(00)gq/99,
PRD(01)gq/00;
Martin et al PRD(01)gq/00 [cosmology];
Rideout PhD(01)gq/02;
Varadarajan & Rideout PRD(06)gq/05 [solution];
Georgiou RSA(05) [random binary growth];
Krugly a1106,
a1112;
Krugly & Stepanian a1111-conf,
Krugly a1201-conf [directed dyadic acyclic graph].
@ Mathematical properties: Alon et al AAP(94) [transitive percolation];
Ash & McDonald JMP(03)gq/02 [characterization],
JMP(05) [Markov chains and posts];
Gudder a1208 [the causal poset is directed but not lattice ordered].
@ Quantum sequential growth models: Gudder a1108,
a1108,
a1204,
a1305,
a1403,
IJTP(14)-a1409;
Surya & Zalel a2003 [criterion for covariance].
Other Proposals
* Example: 2000, An amplitude
exp{−bR} has been tested by Reid & Sorkin, but no published
results.
* Benincasa-Dowker action: The 2D
version is S = N − 2N1
+ 4N2 − 2N3,
where Nm is the number of inclusive orders of
cardinality m + 1.
@ In general:
Wallden JPCS(13) [rev];
Buck et al CQG(15)-a1502 [action, boundary terms];
Gorard a2011 [the Wolfram model and algorithmic dynamics].
@ Action: Sverdlov & Bombelli CQG(09)-a0801 [action in causal set terms, + scalar],
JPCS(09)-a0905 [+ scalar + gauge field];
Benincasa & Dowker PRL(10)-a1001;
Benincasa et al CQG(11)-a1011 [discrete action for a 2D Lorentzian manifold];
Machet & Wang CQG(21)-a2007 [continuum limit];
Dowker a2007 [boundary contributions].
@ Applications: Loomis & Carlip CQG(18)-a1709 [suppression of non-manifold-like sets];
Cunningham & Surya CQG(20)-a1908 [MCMC simulations in 2D and 3D];
Mathur et al a2009 [link action and suppression of KR orders].
@ Other proposals and matter: Criscuolo & Waelbroeck CQG(99)gq/98 [percolation];
Raptis IJTP(00)gq/99 [algebraic quantization];
Blute et al IJTP(03)gq/01 [framework];
Zizzi gq/02;
Foster & Jacobson JHEP(04)ht [2D growing lattice];
Bolognesi a1004 [deterministic];
Gudder a1204,
IJTP(14)-a1303;
Dowker et at CQG(20)-a1910 [manifestly covariant framework, covtree];
Zalel a2008 [structure of covtree].
@ From spin networks:
Markopoulou gq/97,
& Smolin NPB(97)gq,
& Smolin PRD(98)gq/97 [surfaces].
@ Observables: Brightwell et al gq/02-proc,
PRD(03)gq/02;
Dowker & Surya CQG(06)gq/05.
Matter Dynamics > s.a. Anyons [on graphs];
non-local quantum field theories.
* d'Alembertians / wave operators:
2020, of the two main types of proposals, one is defined at each causal set element
with no added structure but is dimension-dependent, while the other is independent
of dimension but requires a choice of preferred past.
@ General references: Kaloper & Mattingly PRD(06)ap [momentum space diffusion];
Mattingly PRD(08)-a0708 [energy-momentum non-conservation];
PRD(09)-a0810 [particle energy-momentum diffusion];
Philpott CQG(10)-a0911 [simulations];
Gudder a1403
[elementary particles as simple c-causets];
Gudder a1507 [quantum particles];
Gudder a1508 [wave equations on c-causets];
Belenchia a1512-MG14;
Alkofer et al PRD(16)-a1605 [Unruh effect];
Dable-Heath et al PRD(20)-a1908 [using perturbative algebraic quantum field theory];
Gogioso et al a2003 [functorial evolution].
@ Particle propagators:
Johnston CQG(08)-a0806,
PRL(09)-a0909 [Feynman propagator];
Johnston CQG(15)-a1411 [correction terms for propagators and d'Alembertians].
@ Scalar fields:
Sverdlov a0807 [bosonic fields];
Dowker et al PRD(10)-a1009 [scalar field propagation];
Belenchia et al JHEP(15)-a1411 [non-local scalar quantum field theory in flat spacetime];
Nomaan X et al CQG(17)-a1701 [scalar field Green functions];
Sverdlov a1805 [field defined over edges, and locality];
Nomaan X a2105-PhD.
@ Other fields: Sverdlov a0807 [gauge theory],
a0808 [spinors],
PhD(09)-a0905;
Scargle & Simić eConf-a0912 [photon dispersion];
Johnston PhD(10)-a1010,
Sorkin JPCS(11)-a1107
[quantum fields on causal set backgrounds in histories-based form];
Sverdlov 12-a1201
[corrections to bosonic-field Lagrangians];
Knuth AIP(13)-a1212,
Noldus a1305 [Fermions and the Dirac equation];
in Alkofer et al PRD(16)-a1605 [Unruh effect];
Glaser CQG(18)-a1802 [coupled 2D Ising model, phase structure];
Sverdlov a1805 [electromagnetic field].
@ d'Alembertians / wave operators: Dowker & Glaser CQG(13)-a1305,
Glaser CQG(14)-a1311
+ CQG+(14),
a1409-PhD;
Aslanbeigi et al JHEP(14)-a1403 [generalized];
Belenchia et al CQG(16)-a1510 [continuum limit];
Belenchia CQG(16)-a1510 [universal behavior].
@ Entanglement entropy: Sorkin & Yazdi CQG(18)-a1611;
Belenchia et al CQG(18)-a1712 [scalar fields on causal sets];
Surya et al a2008 [de Sitter horizons].
Other Phenomenology
@ Cosmology: Ahmed et al PRD(04)ap/02 [unimodular relativity],
comment Barrow PRD(07)gq/06;
Kuznetsov a0706;
Zuntz PRD(08)-a0711 [and the cmb];
Ahmed & Rideout PRD(10)-a0909 [de Sitter space];
Krioukov et al NatSR(12)-a1203 [and the structure of complex networks];
Glaser & Surya a1410 [Hartle-Hawking wave function, 2D];
Dowker & Zalel CR(17)-a1703 [renormalisation of dynamical parameters];
> s.a. hartle-hawking proposal; cosmological
constant; dark matter types.
@ Black holes:
Dou PhD(99)gq/01 [and entropy];
Asato CQG(19)-a1905 [definition based on singular antichains];
Machet & Wang a2012 [horizon entropy];
> s.a. black-hole entropy.
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