Canonical Formulation of General Relativity  

In General > s.a. constraints; initial-value formulation; symmetries in physical theories.
* Idea: Recast the Einstein equation in a form that uses classical states as evolving points on a phase space; The equations themselves are equivalent to those in the initial-value formulation, but the symplectic structure of phase space allows us to study the constraint and symmetry algebra, and to set up the quantum theory.
* Issues: The absence of a preferred time, or multi-fingered nature of time (> see time in gravitation).
* With a spatial boundary: The constraint algebra may acquire a central extension.
@ Introductions and reviews: Bojowald 11; Giulini a1505-in.
@ General: Dirac PRS(58); Teitelboim PLB(75) [gauge choices]; Fischer & Marsden GRG(76); Christodoulou et al GRG(79); Ó Murchadha gq/03 [from first principles]; Lusanna IJGMP(07)gq/06-ln [kinematical basis]; Kiriushcheva & Kuzmin CEJP(11)-a0809 [myths and realities]; Shestakova in(09)-a0911 [unsolved problems]; Fayzullaev IJMPA(10)-a1004; Richter & Plyatsko JPCS(11)-a1303 [hyperbolicity of Hamiltonian formulations]; Montesinos et al a1912 [from Palatini action, with no second-class constraints]; Frolov a2001 [natural form of Hamiltonian].
@ Different versions: Franke TMP(06)-a0710; Frolov et al G&C(11)-a0809; Cianfrani et al PLB(12)-a1104 [relationship between ΓΓ and ADM formulations].

Special Systems and Related Concepts > s.a. observables; specific types of metrics; time in quantum gravity.
@ Asymptotically flat spacetimes: Marolf CQG(96)gq/95; Bartnik gq/04/CAG [Hilbert manifold structure]; Campiglia CQG(15)-a1412 [falloff conditions and consequences]; Corichi & Reyes CQG(15)-a1505 [consistent formulation from Holst action with surface terms].
@ Spatially bounded spacetimes: in Brown & York PRD(93); in Lau CQG(96)gq/95 [boundary momenta]; Soloviev TMP(97)gq/98; Carlip CQG(99)gq [Killing horizon]; Czuchry et al PRD(04)gq [null boundary, and thermodynamics]; Chen et al a1307 [choice of reference metric]; Sun et al proc(17)-a1604 [covariant boundary terms, and quasilocal quantities]; > s.a. hamiltonian systems; quasilocal formulation.
@ Diffeomorphisms: Isham & Kuchař AP(85); Kuchař FP(86); Kuchař & Torre PRD(91) [harmonic gauge]; Stone & Kuchař CQG(92); Antonsen & Markopoulou gq/97; Luo et al PLB(98)gq/97; Kouletsis gq/98; Salisbury et al NPPS(00)gq [Ashtekar variables]; Samuel CQG(00)gq; Bimonte et al IJMPA(03)ht [Peierls brackets]; Pons CQG(03)gq [spacetime]; Salisbury MPLA(03)gq-proc [and symmetries]; Savvidou CQG(04)gq/03, CQG(04)gq/03; Lusanna & Pauri GRG(06)gq/04, GRG(06)gq/04; Kiriushcheva et al PLA(08)-a0808; Kiriushcheva et al IJTP(12)-a1107 ["non-canonicity puzzle" and Lagrangian symmetries of the action]; Salisbury et al IJMPA(16)-a1608 [restoration of 4D diffeomorphism covariance]; > s.a. embeddings [hyperspace]; gauge theories.
@ And time: Ashtekar & Horowitz JMP(84) [canonical choice]; Kouletis PRD(08)-a0803 [generally covariant form]; Christodoulou et al IJMPD(12)-a1206-GRF [negative lapse]; Thébault SHPMP(12) [interpretation, on three denials of time]; Pitts SHPMP(14)-a1406 [change is real and local].
@ Reduction to true degrees of freedom: Kijowski et al PRD(90) [with perfect fluid]; Fischer & Moncrief GRG(96).
@ In extended phase space: Shestakova CQG(11)-a1102, comment Kiriushcheva et al a1107 [and canonical transformations]; Shestakova JPCS(12)-a1111; > s.a. models in canonical gravity.
@ Related topics: Baskaran et al AP(03) [boosts and center of mass]; Wang gq/06 [conformal decomposition]; Anderson a0711 [and relationalism].
> Related theories: see higher-order theories; hamiltonian systems; linearized general relativity; modified theories; teleparallel gravity.

Geometrodynamics > s.a. ADM formulation [including variations]; spacetime [relational].
@ General references: Kuchař JMP(74) [ADM super-Lagrangian for vacuum and scalar field coupling]; Komar IJTP(78).
@ Dynamics as geodesic flow: Misner in(72); Biesiada & Rugh gq/94; Greensite CQG(96)gq/95; Carlini & Greensite PRD(97)gq/96 [and "worldline'' quantization of gravity]; > s.a. chaos in general relativity.

Triad and Tetrad Variables
@ Triads / tetrads: Castellani et al PRD(82); Charap & Nelson CQG(86), CQG(87), et al CQG(88); Goldberg PRD(88); Henneaux et al PRD(89) [and Ashtekar variables]; Kamimura & Fukuyama PRD(90); Seriu & Kodama PTP(90); van Elst & Uggla CQG(97)gq/96 [threading and slicing]; Bañados & Contreras CQG(98)gq/97; Clayton JMP(98)gq/97 [diffeomorphisms], JMP(99)gq/98 [matter]; Lusanna & Russo gq/98, gq/98; Contreras & Zanelli CQG(99)ht; Lusanna & Russo GRG(02)gq/01; Randono CQG(08)-a0805 [covariant]; Kober CQG(11)-a1107 [non-commuting components of the tetrad field]; Barbero et al a2011 [concise symplectic formulation].
@ Constraint algebra: Henneaux PRD(83); Charap & Nelson JPA(83); Hadjer Lagraa et al CQG-a1606 [polynomial constraints obeying a closed algebra].
@ Other topics: Begtsson IJMPA(90) [P and T]; Lusanna NPPS(00)gq/99 [Dirac observables]; Pons et al GRG(00)gq/99 [gauge group]; Lagraa & Lagraa GRG(18)-a1706 [with fermions].

Other Approaches > see lattice gravity [canonical simplicial gravity]; modified formulations [different variables or splittings, null infinity, covariant formulations including coupling to matter].

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