Types of Approaches to Quantum Gravity  

Group Field Theory > s.a. deformed special relativity; renormalization; tensor networks.
@ General references: Oriti JPCS(06)gq/05, in(09)gq/06; Freidel IJTP(05)ht; Ryan gq/06 [new proposal]; Oriti JPCS(07)ht/06, a0709-proc, a0710-proc; Oriti CQG(10)-a0902 [and simplicial quantum gravity], JPCS(09)-a0903; Oriti & Tlas CQG(10)-a0912 [simplicial quantum geometry]; Oriti a0912-proc [rev]; Oriti & Sindoni NJP(11)-a1010-in [hydrodynamics, and classical geometrodynamics]; Vitale PoS-a1103 [relationship with discretized BF models]; Livine et al CQG(11)-a1104 [and the canonical Hamiltonian constraint]; Oriti a1110-ch [introduction]; Baratin & Oriti JPCS(12)-a1112 [non-technical]; Vitale AIP(12)-a1203 [rev]; Carrozza PRD(15)-a1411 [in dimension 4 – ε]; Kotecha & Oriti NJP(18)-a1801 [Gibbs states]; Wilson-Ewing PRD(19)-a1810 [relational Hamiltonian]; Oriti a1811 [I]; Carrozza et al Univ(20)-a2001 [overview].
@ And lqg / lqc: Oriti & Tlas CQG(08)-a0710 [unifying framework for lqg and simplicial quantum gravity]; Oriti CQG(16)-a1310 & CQG+ [as the 2nd quantization of lqg]; Oriti a1408-in [lqg]; Oriti et al NJP(15)-a1409 [for the whole loop quantum gravity state space].
@ Quantum cosmology: Gielen et al PRL(13)-a1303; Calcagni PRD(14)-a1407 [lqc]; Gielen & Sindoni Sigma(16)-a1602; Gielen CQG(16)-a1604 [from GFT condensate]; de Cesare et al PRD(16)-a1606 [cyclic universe and accelerated expansion]; Oriti a1612-CRP [intro]; de Cesare et al CQG(18)-a1709, Gielen & Oriti PRD(18)-a1709 [cosmological perturbations]; Baytaş et al Univ(19)-a1811 [and lqc]; Pithis & Sakellariadou Univ(19)-a1904 [rev].
@ With matter: Li et al CQG(17)-a1703 [scalar field]; Gielen a1808 [in a matter reference frame].
@ Related topics: Pithis & Thürigen a1808 [phase transitions, Landau perspective].

Other Approaches > s.a. emergent gravity; physical theories; non-commutative gravity; spacetime topology; stochastic quantum mechanics; quaternions.
@ Conformal factor: Padmanabhan PRD(83), PRD(83); Bleecker CQG(87); Floreanini & Percacci NPB(95) [effective potential]; Antoniadis et al PRD(97)ht/95, PRD(97)ht/95; in Burdet & Perrin gq/97; Shojai et al MPLA(98)gq/99; Shojai IJMPA(00)gq [??]; 't Hooft a1009 [integrating over the conformal factor first]; Hamada PRD(12).
@ Geodesic distance, metric uncertainty: Diósi & Lukács PLA(89); Álvarez et al PLB(92) [geodesic distance as variable], PRD(92) [quantum metric space]; Maggiore PLB(93)ht; Chiang et al PRD(16)-a1512 [spacetime interval operator]; Padmanabhan MPLA(20)-a1911; > s.a. world function.
@ Covariant Hamiltonian: Kanatchikov gq/98-proc, gq/99, IJTP(01)gq/00 [de Donder-Weyl]; Aleksandrov TMP(04) [covariant lqg].
@ Theory of embeddings: Pavšič CQG(85)-a1403, FP(96)gq/95, G&C(96)gq/95; Hájíček & Kiefer NPB(01)ht/00 [spherical shell]; Park ATMP(18)-a1406 [hypersurface foliation].
@ And spinor fields: Lisi gq/02; Galehouse in(04)mp/02; Kober PRD(09)-a0812; Hughes & Randono a1105 [is geometry bosonic or fermionic?]; Vladimirov & Diakonov PRD(12)-a1208 [phase transitions in spinor quantum gravity on a lattice]; > s.a. canonical quantum gravity; spin networks.
@ Local: Noldus a1101; Larsson a1407 [diffeomorphism symmetry, unitarity, and locality postulated]; Palmer a1709.
@ Quasilocal: Conrady et al PRD(04)gq/03 [vacuum].
@ Based on fluctuations: Zakir ht/98, ht/99; Hu IJTP(02)gq [kinetic theory of fluctuations]; Hall GRG(05) [from "exact uncertainty"]; Succi IJMPC(12)-a1111 [Kolmogorov scaling theory, turbulence, and fractal spacetime]; > s.a. quantum spacetime; stochastic quantization.
@ Newtonian: Hansson PE(10)gq/06; Bramson PRS(07) [axisymmetric, spinning systems].
@ Algebraic methods: Crane JMP(95)gq; Tanasa CQG(10)-a0909; Martins IJMPA(13)-a1003 [overview]; Etesi ATMP(16)-a1402 [and orientation-preserving diffeomorphism group]; Giddings JHEP(15)-a1503 [Hilbert space structure, non-locality and entanglement]; Araya-Gochez a1601 ["quantum ring theory"]; Rejzner IJMPD(16)-a1603-MG14 [perturbative]; Freidel et al a2007 [corner symmetry algebra].
@ Renormalizable theory proposals: Krasnov ht/06 [non-metric]; Wiesendanger JModP(14)-a1308 [gauge theory of volume-preserving diffeomorphisms], CQG(19)-a1806 [gauge theory of the Lorentz group].
@ And gauge theory: Ragiadakos a1204-GRF [Lorentzian complex structure of spacetime]; Hanada a1407-conf [gauge-gravity duality and super Yang-Mills theory]; > s.a. covariant quantum gravity; types of gauge theory [higher gauge theory].
@ Precanonical quantization: Kanatchikov NPPS(00)gq, IJTP(01)gq/00, AIP(13)-a1212, NPCS-a1407, a1512-MG14; > s.a. approaches to canonical qg.
@ Related topics: Banks NPB(85); Gotay CQG(86); Casher PLB(87); Kleinert PLB(87); Kocharovsky & Kocharovsky FP(87); Balbinot et al PRD(90) [and adiabatic phase]; Myers CQG(92) [unbounded action]; Greensite PRD(94)gq/93 [transfer matrix formalism]; Galehouse qp/94; Modanese NPB(95) [potential energy]; Prugovečki in(96)gq/95 [quantum frame bundles]; Federbush ht/99; Dzhunushaliev & Singleton Ent(02)gq/01 [and complexity]; Nishikawa ht/02-conf [minimal assumptions]; Minic & Tze PLB(04)ht/03, ht/04-proc; Moffat gq/04 [in momentum space]; Jejjala et al IJMPD(04)gq [??]; Iftime DGDS-gq/07; Nassif a0709 [at large length scales]; Finkelstein IJTP(08) [homotopy]; Glinka G&C(10)-a0808; Darabi a0809 [phenomenological]; Yang MPLA(10)-a1007; Yang a1111-proc ["background-independent"]; Takook & Rouhani a1208 [Krein space quantization]; Palmer a1210 ["gravitational theory of the quantum"]; news ns(13)may [Weinstein's theory of everything]; Salvio & Strumia JHEP(14)-a1403, EPJC(18)-a1705 [without scales, "agravity"]; Sutherland a1502 ["naive", using final boundary conditions]; Mandrin a1505 [non-dynamical approach, NDA]; Walstad a1507 [from special relativity and quantum theory]; Horndeski a1508 [with gravitons as holes in space]; Arbuzov et al PAN(17)-a1511 [Von Neumann's procedure]; > s.a. decomposition; Dirac Sea; duality [gauge-gravity, surface-state]; holography in gravitation; renormalization and asymptotic safety; Third Quantization.

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