Connection-Based Formulations of General Relativity| Connection-Based Formulations of General Relativity |
In General
> s.a. ashtekar-variables formulation (lqg variables);
gauge theories of gravity.
* Idea: Formulations
in which the main variables include a connection and possibly other
fields, but not a metric.
@ Affine connection:
Kijowski & Werpachowski RPMP(07)gq/04;
Poltorak gq/04-GR17;
Popławski GRG(14)-a1202;
Castillo-Felisola & Skirzewski RMF-a1410.
@ GL(4)-invariant form:
Floreanini & Percacci CQG(90),
CQG(90).
@ Connection + scalar density:
Capovilla et al PRL(89),
CQG(91);
Capovilla & Jacobson MPLA(92)gq;
Bengtsson & Peldán PLB(90);
Peldán PLB(90) [with matter];
Bengtsson PLB(91);
Dadhich et al CQG(91).
@ Two connections: Barbero IJMPD(94)gq/93,
PRD(94)gq/93.
@ Two-forms: Plebański JMP(77);
Bengtsson gq/93,
CQG(95)gq;
Katsuki et al IJMPA(96) [BF theory, quantum gravity];
Pillin CQG(96) [and matter];
Grant gq/97 [self-dual];
Lewandowski & Okołów CQG(00)gq/99;
Krasnov GRG(11)-a0904 [pedagogical];
Capovilla et al CQG(10)-a1004 [Krasnov's generalization];
> s.a. BF theories; 1st-order actions;
gravity.
@ Other versions: Floreanini & Percacci CQG(91) [GL(3) connection + other];
Kozameh & Newman GRG(91);
Capovilla et al CQG(91),
Robinson CQG(96)
[sl(2, \(\mathbb C\))-valued connection, and forms],
JMP(03) [generalized forms];
Miković & Vojinović CQG(12)-a1110 [as a constrained topological theory of the Poincaré 2-group];
Mol AACA(17)-a1406 [non-metricity formulation];
González & Montesinos PRD(15)-a1501 [SO(3, \(\mathbb C\)) gauge connection and complex-valued 4-form];
Robinson a1506 [generalized differential forms].
Connection + Spinorial / Vierbein Variables
> s.a. approaches to canonical quantum gravity; initial-value
formulation; loop variables; Metric-Affine Gravity.
@ General references:
Deser & Isham PRD(76);
Dubois-Violette & Madore CMP(87);
Obukhov & Tertychniy CQG(96);
Clayton CQG(97)gq/06 [constraint algebra];
Lusanna & Russo gq/98,
gq/98;
Aldrovandi & Barbosa gq/02 ["spacetime skeleton"];
Aldrovandi et al GRG(03)gq [gravity as anholonomy],
gq/04-proc;
Kummer & Schütz EPJC(05)gq/04;
Estabrook PRD(05)gq/04 [structure of vacuum equations],
CQG(06)gq/05 [conservation laws];
Zinoviev JHEP(06)ht/05,
ht/05 ["dual" formulation];
Cianci et al CQG(05)mp,
IJGMP(06)mp;
Wang PRD(05)gq;
Abou-Zeid & Hull JHEP(06) [chiral expansion];
Itin a0711-ch [coframe];
Yepez a1106 [Einstein's 1928 proposal];
Socolovsky a1110;
Ivancevic a1111-wd
[SL(2, \(\mathbb C\)) connection and 2 spinor-valued 1-forms, matter interactions];
> s.a. canonical general relativity.
@ With fermions: Fatibene et al GRG(98);
Canarutto JMP(98) [including degenerate tetrad];
Godina et al GRG(00).
@ With bosons: Fatibene et al GRG(99).
@ Generalized:
Abe IJMPA(90) [supersymmetric].
Related Formulations
@ Bundle of Frames version: (2 × 2 matrix)
Chinea PRL(84);
Chinea & Guil JMP(85).
@ Other forms: Herfray JMP(17)-a1610 [chiral formulations and twistor action].
main page
– abbreviations
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send feedback and suggestions to bombelli at olemiss.edu – modified 17 jan 2021