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.
@ 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; Gudder a1108, a1108 [quantum]; Krugly & Stepanian a1111-conf, Krugly a1201-conf [directed dyadic acyclic graph]; Gudder a1204, a1305, a1403, IJTP(14)-a1409 [quantum sequential growth].
@ 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].

Other Proposals
* Example: 2000, An amplitude exp{−bR} has been tested by Reid & Sorkin, but no published results.
@ General references: Wallden JPCS(13) [rev]; Buck et al CQG(15)-a1502 [action, boundary terms].
@ Sum over histories: Loomis & Carlip CQG(18)-a1709 [suppression of non-manifold-like sets].
@ Other proposals and matter: Criscuolo & Waelbroeck CQG(99)gq/98 [percolation]; Raptis IJTP(00)gq/99; Blute et al IJTP(03)gq/01 [framework]; Zizzi gq/02; Foster & Jacobson JHEP(04)ht [2D growing lattice]; Sverdlov & Bombelli CQG(09)-a0801 [action in causal set terms, + scalar], JPCS(09)-a0905 [+ scalar + gauge field]; Bolognesi a1004 [deterministic]; Gudder a1204, IJTP(14)-a1303.
@ 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.
@ Related topics: Benincasa et al CQG(11)-a1011 [discrete action for a 2D Lorentzian manifold].

Matter Dynamics > s.a. non-local quantum field theories.
@ 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].
@ 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].
@ 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]; 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: 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].

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. boundary conditions in quantum cosmology; cosmological constant; dark matter types.
@ Black holes: Dou PhD(99)gq/01 [and black-hole entropy]; > s.a. black-hole entropy.

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