Canonical Formulation of General Relativity| 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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