Einstein-Cartan Theory  

In General > s.a. gravity theories / first-order actions for general relativity.
* 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: It was 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; It can also be described as a constrained BF theory.
@ General references: Hehl et al RMP(76); Fiziev in(96)gq/97 [Lagrangian]; Dzhunushaliev & Singleton PLA(99)gq/98; Trautman en(06)gq [rev]; Fabbri AFLB(08)-a0808 [uniqueness]; Popławski AR(13)-a1106 [in gravity and cosmology]; Socolovsky a1110 [in terms of bundles and connections]; Popławski fn(12)may [and universe inside a black hole]; Pilc a1311 [kinematical description].
@ Hamiltonian formulation: Szczyrba CMP(78); Nikolić CQG(95) [and constraints].
@ Merits / objections: Hehl gq/97-MG8; in Ohanian & Ruffini 94, p312; Diether & Christian a1705 [and fundamental particle physics].
@ Tests: Garcia de Andrade CQG(01).
> Online resources: see Wikipedia page.

Special Systems and Phenomenology > s.a. metric matching; particle models.
@ Monopoles: Garcia de Andrade gq/99, gq/99 [+ dilaton]; Rahaman et al NCB(05).
@ Cosmological models: Garcia de Andrade gq/00, PLB-gq/00; Galiakhmetov G&C(09) [rotating and expanding cosmologies], CQG(10) [k = 0 FLRW models + non-minimal scalar field]; Popławski a1201 [thermal fluctuations and cosmological perturbations]; Magueijo et al PRD(13)-a1212 [with Holst term and fermions]; Bravo Medina et al AP(19)-a1812; > s.a. bianchi I, bianchi IX and other bianchi models; cosmological acceleration in modified theories; cosmology in modified gravity.
@ Other systems: Bressange CQG(00) [thin shells]; Farfán et al GRG(12)-a1101 [non-static, spherically symmetric solutions].

Related Topics and Theories > s.a. canonical formulations of gravity [covariant]; torsion in physical theories.
@ General references: Castagnino et al GRG(85), Castagnino & Levinas GRG(87) [post-newtonian approximation]; Singh & Ryder CQG(97) [low-energy theory]; Ruggiero & Tartaglia AJP(03)dec-gq [as a theory of spacetime defects]; Popławski a1001 [no extra dimensions].
@ Coupled to a Maxwell field: Popławski IJTP(10)-a0905; Popławski a1108.
@ With other fields: Hammond GRG(95) [Einstein-Cartan-Proca]; Xue PLB(08) [four-fermion interaction, phase structure]; Kaźmierczak PRD(09) [with Holst term and fermions]; Lagraa & Lagraa CQG(10)-a0908 [fermions]; Khanapurkar a1803-MS [Dirac field, minimal coupling]; Chen et al a1912 [ambiguity in matter couplings]; > s.a. types of spinors [ELKO spinors].
@ And other gravity theories: Petti GRG(86)-a1301 [derivation from general relativity]; Botta Cantcheff PRD(08)-a0801 [for Chern-Simons Lorentz-violating gravity]; Baekler & Hehl CQG(11)-a1105 [Lagrangians with quadratic torsion and curvature terms].
@ Quantum theory: Xue PLB(09)-a0902, PRD(10)-a0912 [Regge calculus]; Pilc a1312 [kinematical Hilbert space]; Shapiro & Teixeira CQG(14)-a1402 [with Holst term in the action]; Cianfrani a1605 [physical states]; > s.a. Schwinger's Principle.
> Related topics: see Metric-Affine Gravity; Mimetic Gravity; poincaré group [gauge invariance]; spacetime singularities.

main pageabbreviationsjournalscommentsother sitesacknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 15 jul 2020