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; Skirzewski & Castillo-Felisola 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 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 [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 a1610 [chiral formulations and twistor action].


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