Canonical Formulation of General Relativity

In General > s.a. constraints; initial-value formulation; specific types of metrics.
* Idea: Recast the Einstein equation in a form that uses classical states as evolving points on a phase space.
* Issues: The absence of a preferred time, or multi-fingered nature of time (> time in gravitation).
* With spatial boundary: The constraint algebra may acquire a central extension.

References > s.a. modified theories [strong coupling]; observables; time in quantum gravity; {AA notes}.
@ 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 gq/06-ln [kinematical basis]; Franke TMP(06)-a0710 [different versions].
@ Asymptotically flat metrics: Marolf CQG(96)gq/95; Bartnik gq/04 [Hilbert manifold structure].
@ Diffeomorphisms: Isham & Kuchar AP(85); Kuchar FP(86); Kuchar & Torre PRD(91) [harmonic gauge]; Stone & Kuchar 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-in [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); > s.a. embeddings [hyperspace], gauge theories.
@ And time: Ashtekar & Horowitz JMP(84) [canonical choice]; Kouletis a0803.
@ Reduction to true degrees of freedom: Kijowski et al PRD(90) [with perfect fluid]; Fischer & Moncrief GRG(96).
@ And histories formulation: Savvidou gq/04-in; Savvidou CQG(06)gq [Barbero connection].
@ Spatially bounded: 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]; > s.a. hamiltonian systems, quasilocal.
@ Related topics: Baskaran et al AP(03) [boosts and center of mass]; Wang gq/06 [conformal decomposition]; Anderson a0711 and relationalism].
> For other theories: see higher-order theories; hamiltonian systems; linearized general relativity; teleparallel.

Geometrodynamics > s.a. ADM formulation; spacetime [relational].
@ General references: Kuchar JMP(74) [ADM super-Lagrangian for vacuum and scalar field coupling].
@ 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 a0805 [covariant].
@ Constraint algebra: Henneaux PRD(83); Charap & Nelson JPA(83).
@ Other topics: Begtsson IJMPA(90) [P and T]; Lusanna NPPS(00)gq/99 [Dirac observables]; Pons et al GRG(00)gq/99 [gauge group].

Other Variables > s.a. 3D general relativity; 3D gravitation; quasilocal gravity.
* Idea: In a slicing (as opposed to threading) approach to canonical gravity, one chooses a (C^infty) 3-manifold which will act as the (unchanging) spatial manifold, and encodes all the information necessary to reconstruct a spacetime metric into a set of fields defined on .
@ General references: Peldán CQG(91) [non-uniqueness of Hamiltonian]; Tate CQG(92); Lewandowski & Okolów CQG(00)gq/99 [2-form, BF-like]; Farajollahi & Luckock GRG(02)gq/01 [and local observer].
@ Embedding variables, reference fluid: Kuchar PRD(92); Braham PRD(94)gq/93 [cylindrical symmetry]; Brown gq/94-in; Brown & Kuchar PRD(95)gq/94 [and time]; Montani & Zonetti IJMPA(08)-a0807.
@ Dirac eigenvalues: Landi & Rovelli PRL(97)gq/96; Landi gq/99-in; > s.a. supergravity.
@ Spinorial variables: Grant CQG(99)gq/98 [any dimension].
@ Other variables: Rosas-Rodríguez gq/05 [electric and (complex) magnetic fields]; Katanaev TMP(06)gq [including det g].
> Connection dynamics: see connection and loop variable formulation.

Other Approaches > see modified formulations [different splittings of spacetime, null infinity, covariant formulations].

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