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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