2-Dimensional Quantum Gravity

Based on General Relativity > s.a. [2D gravity, quantum gravity]; modified general relativity [strong coupling limit]; regge calculus.
* Lorentzian vs Euclidean: The non-perturbative path integral can be computed exactly, and one sees that the two theories yield completely different results; The causal structure seems to play an important role.
@ Reviews: Kummer gq/05-in.
@ General references: Rajeev PLB(82); Martinec PRD(84) [+ scalar matter]; Hartle CQG(85); Knizhnik et al MPLA(88) [fractal structure]; Awada & Chamseddine PLB(89) [partition function]; Isler & Trugenberger PRL(89); Polchinski NPB(89); D'Hoker MPLA(91) [and Liouville]; Weis ht/98-PhD [topological]; Ambjørn et al PLB(06)gq [and emergence of background geometry].
@ Canonical: Banks & Susskind IJTP(84) [synchronous gauge]; McKeon CQG(06).
@ Canonical, with matter: Vergeles JETP(00)gq/01 [scalar + Majorana field]; Mann & Young CQG(07)gq/06 [particles].
@ Lorentzian vs Euclidean: Ambjørn & Loll NPB(98)ht; Aldaya & Jaramillo CQG(00)gq/99; Ambjørn et al CSF(99)ht/98, PLB(00)ht/99.
@ Path integral: Muslih GRG(04) [Hamilton-Jacobi based]; > s.a. regge calculus [measure].
@ Path integral, Lorentzian: Loll et al NPPS(00)ht/99; Loll & Westra CQG(06)ht/03, APPB(03)ht-in [sum over topologies].
@ Spin foam: Livine et al CQG(03)gq/01 [manifold-independent]; Oriti et al CQG(05)gq/04 [as constrained BF theory].
@ Other approaches: Benedict PLB(94)gq [gauge theory and geometrical methods]; Benedict et al PRD(96) [functional Schrödinger and BRST]; Lavrov & Moshin CQG(99) [BV and BLT, with torsion].
@ Simulations: Ambjørn et al PRD(99)ht [with matter], PRD(00)hl/99 [with conformal field theory, phase transitions].
@ With Ising matter: Bowick et al PLB(97) [Hausdorff dimension].
@ With cosmlogical constant: Govaerts ht/02 [cosmological constant quantization].

Related Topics > s.a. spacetime topology.
@ Black holes: Grumiller et al NPB(00) [virtual]; Frolov et al PRD(05)ht [dilaton + abelian gauge theory, semiclassical]; > s.a. semiclassical general relativity.
@ Time: Ambjørn et al JHEP(98)ht [and fractal dimension].
@ Branched polymer phase: Jonsson & Wheater NPB(98) [spectral dimension].
@ Other topics: Ambjørn et al JHEP(99)hl/98 [correlations and order], PLB(06) [fluctuations and background geometry].

Dilaton Theories > s.a. [2D gravity]; dilaton.
@ General references: Seiler & Tucker PRD(96) [reduced phase space]; Louis-Martinez PRD(97) [exact states]; Grumiller & Kummer gq/03-in [background-independent].
@ Dirac quantization: Louis-Martinez et al PLB(94)gq/93; Kuchar et al PRD(97)gq/96 [collapse]; Laddha CQG(07)gq/06, CQG(07) [polymer quantization of CGHS model].
@ Path integral: Kummer et al NPB(97)gq/96; Kummer et al NPB(98)ht/97, NPB(99)ht/98, Grumiller gq/01-PhD [with scalar matter]; Meyer ht/06-in [with Dirac fields]; Bergamin & Meyer a0711-in [with boundary].
@ Trace anomaly: Bousso & Hawking PRD(97)ht, comment Kummer et al PRD(98)ht.

Other Theories > s.a. 2D gravity; Liouville Theory; non-commutative field theory.
@ References: Polyakov & Zamolodchikov MPLA(88) [fractal structure]; Strobl PRD(94) [R² gravity + Yang-Mills]; Amelino-Camelia et al PLB(95)ht [area-preserving diffeomorphisms and anomalies]; Constantinidis et al PRD(09)-a0812 [Jackiw-Teitelboim theory].

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