Torsion in Physical Theories  

In General > s.a. torsion.
* Motivation: Torsion arises in string theory as an antisymmetric field, and would be required by the modification of general relativity that can accomodate the existence of gravitomagnetic monopoles.
* Minimal coupling: Requires that the trace of the torsion tensor be a gradient, Ta = a, and that the modified volume element = exp{} |g| dx1 ... dxn be used in the action formulation of a physical model.
@ General references: Hehl & Obukhov a0711 [geometry and field theory].
@ Dynamics of torsion: Saa GRG(97)gq/96; Mosna & Saa JMP(05)gq [minimal coupling]; Poplawski gq/06, JMP(06).
@ Singularities: García de Andrade FP(90), IJTP(90); Esposito NCB(90)gq/95, FdP(92)gq/95.
@ Topological defects: Letelier CQG(95)gq; Garcia de Andrade MPLA(97), JMP(98)gq/98, gq/98 [domain walls], gq/99/PRD; Anandan gq/99-in.
@ And electromagnetism: Hammond GRG(88), GRG(91); Horie ht/95; de Andrade & Pereira IJMPD(99)gq/97; Filewood gq/98; Rubilar et al CQG(03) [and birefringence].
@ Angular momentum conservation: Yishi Duan & Ying Jiang GRG(99)gq/98; Capozziello et al EPL(99)ap [fermion helicity flip].
@ And topological invariants: Aouane et al CQG(07) [from integral of Nieh-Yan 4-form]; Nieh IJMPA(07) [rev].
> Specific theories: see dirac fields in curved spacetime; field theories; particle models; schwarzschild.
> Related topics: see lagrangian theories; lorentz invariance; regge calculus; sound [acoustic torsion].

And Gravity > s.a. gravitation.
* Couplings and gravity: In general, torsion couples to the spin current of the Dirac field; In the teleparallel theory of gravity, curvature and torsion are alternative ways of describing the gravitational field, and are consequently related to the same degrees of freedom; More general gravity theories, like Einstein-Cartan and gauge theories for the Poincaré and the affine groups, consider curvature and torsion as representing independent degrees of freedom.
@ General references: Hehl et al RMP(76); Penrose FP(83); Hehl FP(85); Hammond GRG(90), GRG(94), GRG(94), CP(95) [II]; Gangopadhyay & Sengupta ht/97 [symmetries]; Fiziev gq/98-in, gq/98; Israelit FP(98)-a0712, in(99)-a0712 [and electromagnetism]; de Sabbata & Ronchetti FP(99) [Hamiltonian]; Megged ht/00 [gravity + Yang-Mills]; Garecki RGC(04)gq/01 [overview, T not needed]; Mahato MPLA(02)gq/06 [G in Riemann-Cartan spacetime]; Watanabe & Hayashi gq/04; Arcos & Pereira CQG(04), IJMPD(04)gq/05 [rev]; Mahato IJMPA(07)gq/06; Kim & Pak CQG(08)-gq/06 [quantum gravity]; Lecian et al gq/07-in; Aldrovandi & Pereira a0801-AFLB [rev]; Schücking a0803 [Einstein's theory is about torsion].
@ Connection formulation: Montesinos JMP(99) [and Ashtekar–Barbero connection].
@ Higher-order theories: Hammond JMP(89), JMP(90) [second-order equations]; Troncoso & Zanelli CQG(00)ht/99; Kruglov a0710 [quantum]; Capozziello et al CQG(07) [metric-affine].
@ Higher-dimensional theories: Mukhopadhyaya et al PRD(02) [large extra dimensions], PRL(02) [in Randall-Sundrum scenario].
> Specific types of theories: see 2D gravity; 3D gravity; action for general relativity; einstein-cartan; teleparallel.

Phenomenology > s.a. bianchi models; brans-dicke; CPT; tests of general relativity [precession]; wormholes.
* Particle motion: Notice that, in a manifold with torsion, geodesics as extremal lines do not coincide with autoparallels.
* Idea: The question whether there is torsion in the physical world is not settled; There is an issue of which notion of geodesics (extremal or autoparallel) is the appropriate one for test particle geodesics.
* Bounds: The axial torsion K 1.5 × 10–15 m–1 [@ Lämmerzahl PLA(97)].
@ Particle motion: Kleinert & Pelster GRG(99)gq/96; Kleinert GRG(00)gq/98, GRG(00)gq/98; Shapiro ht/98-in, PRP(02)ht/01 [rev]; Sivaram & Garcia de Andrade gq/01; Aprea et al IJMPD(03)gq/04; Arcos et al IJMPD(04)gq; > s.a. higher-spin fields, spinning particles.
@ Other hep effects: Alimohammadi & Shariati MPLA(99), Adak et al CQG(01)gq [ oscillations], PRD(04)gq/03 [and non-metricity]; Abel & Owen NPB(03) [CP violation, CKM matrix]; Khriplovich & Pomeransky PRD(06)ht/05 [spinning particles, Immirzi parameter].
@ Gravitation: de Andrade et al gq/04-in [coupling, and Dirac spinor]; Aros & Contreras PRD(06)gq [black holes]; Chen a0705.
@ Cosmology: Capozziello et al gq/01-in, Watanabe & Hayashi gq/04 [acceleration]; Wanas a0705, IJMPA(07)-a0802 [torsion energy]; > s.a. acceleration, frw models.
@ Torsion waves: Hammond GRG(97); Babourova et al CQG(99)gq/98; King & Vassiliev CQG(01)gq/00 [and neutrinos].
@ Experimental evidence: Zhang et al GRG(92); Lämmerzahl PLA(97)gq [Hughes-Drever experiment]; Garcia de Andrade gq/01 [gravitational radiation detectors]; Mao et al PRD(07)gq/06, Flanagan & Rosenthal PRD(07)-a0704 [PPN-like formalism, and Gravity Probe B]; Pereira a0704-in [possible interpretations]; Kostelecky et al PRL(08)-a0712 [bounds from searches of Lorentz violation with fermions]; Russell a0803-in [similarities with Lorentz violation].

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