Einstein-Cartan Theory

In General > s.a. gravity theories.
* Idea: A theory of gravity coupled to a 4-spinor field through a connection, sometimes also associated with the names of Sciama and Kibble; Variables are a tetrad, a connection, and a spinor field; The theory necessarily has torsion, and is not equivalent to one in which one imposes that the connection be one defined by the metric (Einstein-Dirac); For simple (non derivative-coupled) sources (vanishing torsion) it is equivalent to general relativity.
* History: Proposed in 1922, before the discovery of spin, by Élie Cartan, who was influenced by the 1909 work of the Cosserat brothers, who considered besides an (asymmetric) force stress tensor also a moments stress tensor in a suitably generalized continuous medium.
* And observation: Torsion effects are probably not observable classically.
* Versions: The theory can be reformulated in 3+1 form using 2-spinors; It is then equivalent to the self-dual version with appropriate reality conditions.
@ General references: Hehl et al RMP(76); Fiziev in(96)gq/97 [Lagrangian]; Dzhunushaliev & Singleton PLA(99)gq/98; Trautman gq/06-in [rev].
@ Hamiltonian formulation: Szczyrba CMP(78); Nikolic CQG(95) [and constraints].
@ Merits / objections: Hehl gq/97-MG8; in Ohanian & Ruffini 94, p312.
@ Tests: Garcia de Andrade CQG(01).

Special Systems > s.a. bianchi I, bianchi IX and other models; metric matching; particle models.
@ Monopoles: Garcia de Andrade gq/99, gq/99 [+ dilaton]; Rahaman et al NCB(05).
@ Other systems: Garcia de Andrade gq/00, gq/00/PLB [cosmology]; Ruggiero & Tartaglia AJP(03)gq [as theory of spacetime defects]; Bressange CQG{00) [thin shells].

Related Topics and Theories > see canonical formulations of gravity [covariant]; Metric-Affine gravity; torsion.
@ General references: Castagnino et al GRG(85), Castagnino & Levinas GRG(87) [post-newtonian approximation]; Singh & Ryder CQG(97) [low-E theory]; > s.a. spacetime singularities.
@ With other fields: Hammond GRG(95) [Einstein-Cartan-Proca]; Xue PLB(08) [four-fermion interaction, phase structure]; > s.a. spinors [ELKO spinors].
@ And other gravity theories: Botta Cantcheff a0801 [for Chern-Simons Lorentz-violating gravity].

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