Torsion in Physical Theories| Torsion in Physical Theories |
In General
> s.a. torsion; torsion phenomenology.
* 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: It requires that the
trace of the torsion tensor be a gradient, Ta
= ∂aθ, and that the modified volume element
τ = exp{θ} |g| dx1
∧ ... ∧ dxn be used in the action
formulation of a physical model.
* Electromagnetism: The coupling
of torsion to the Maxwell field can be introduced in the Lagrangian density
where q is a parameter, which leads to a modified photon dispersion relation.
@ General references: Kalinowski IJTP(81) [and gauge theory, from Kaluza-Klein theory];
Hehl & Obukhov a0711 [geometry and field theory];
issue AFLB(07)#2-3;
Lazar & Hehl FP(10)-a0911 [Cartan's spiral staircase and the gauge theory of dislocations];
Bergman a1411
[internal symmetry of a metric-compatible spacetime connection];
Lahiri a2005-GRF [contorsion and effective fermion mass].
@ Dynamics of torsion: Saa GRG(97)gq/96;
Mosna & Saa JMP(05)gq [minimal coupling];
Popławski gq/06,
JMP(06);
> s.a. differential forms.
@ Singularities: García de Andrade FP(90),
IJTP(90);
Esposito NCB(90)gq/95,
FdP(92)gq/95.
@ 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];
Prasanna & Mohanty GRG(09) [photon propagation];
Popławski a1108;
Mannheim JPCS(15)-a1406 [magnetic monopoles and Faraday's law, Grassmann numbers].
@ Other matter fields: Fabbri IJTP(18)-a1803 [spinor fields, non-causal propagation];
Fabbri & Tecchiolli MPLA(19)-a1811 [torsion-spinor interaction];
Barrientos et al a1903 [wave propagation];
Delhom EPJC-a2002 [minimal coupling].
@ 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].
Related topics:
see lagrangian theories; lattice field theory;
lorentz invariance; modified uncertainty
relations; regge calculus; sound [acoustic torsion].
And Gravity, Theory
> s.a. 2D gravity; 3D gravity;
gravitation; Affine Gravity;
Metric-Affine Gravity; MOND;
non-commutative gravity.
* Idea: A consistent theory of gravity
with torsion emerged during the early 1960s as a gauge theory of the Poincaré group,
which incorporates as the simplest viable cases the Einstein-Cartan(-Sciama-Kibble) theory,
the teleparallel equivalent general relativity, and general relativity itself.
* Couplings and gravity:
It has been established that torsion couples to the spin of elementary particles
(spin current of the Dirac field), and not to the particles' orbital angular momentum;
The inclusion of torsion in the gravitational formalism leads to four-fermion interactions
(though strongly suppressed in 4D).
* Gravity: 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.
@ Books / Reviews:
de Sabbata & Sivaram 94;
Arcos & Pereira IJMPD(04)gq/05;
Aldrovandi & Pereira AFLB(07)-a0801.
@ General references: Hehl et al RMP(76);
López IJTP(77);
Penrose FP(83);
Hehl FP(85);
Hammond GRG(90),
GRG(94),
GRG(94),
CP(95) [II];
Gangopadhyay & Sengupta ht/97 [symmetries];
Fiziev gq/98-conf,
gq/98;
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);
Mahato IJMPA(07)gq/06;
Lecian et al gq/07-MGXI;
Schücking a0803 [Einstein's theory is about torsion];
Torres-Gómez & Krasnov PRD(09)-a0811 [theory with no black holes];
Lledó & Sommovigo CQG(10)-a0907;
Kleinert EJTP(10)-a1005;
Hammond GRG(10)
= IJMPD(10) [torsion is necessary];
Gaitan IJMPA(10)-a1009 [contortion as a dynamical variable, Yang-Mills formulation];
Garecki a1110-talk [updated overview, T not needed];
Fabbri GRG(13);
Olmo & Rubiera-García PRD(13)-a1306 [in Palatini theories of gravity];
Fabbri a1703 [foundational approach];
Diether & Christian PsJ-a1903
[existence and non-propagation of gravitational torsion];
Chakrabarty & Lahiri EPJP(18)-a1907 [and matter];
Spindel a2102.
@ Connection formulation:
Montesinos JMP(99) [and Ashtekar-Barbero connection];
Iosifidis et al GRG(19)-a1810 [duality between torsion and non-metricity].
@ Hamiltonian analysis:
de Sabbata & Ronchetti FP(99);
Yang et al PRD(12)-a1201
[R + T 2 action].
@ And quantum gravity: Kim & Pak CQG(08)-gq/06;
Singh CS(15)-a1512.
@ With other fields: Israelit FP(98)-a0712,
in(99)-a0712 [and electromagnetism];
Megged ht/00 [gravity + Yang-Mills];
Popławski IJTP(10) [Einstein-Maxwell-Dirac theory];
Fabbri & Vignolo AdP(12)-a1201,
Fabbri IJMPD(13)-a1211,
IJGMP(15)-a1409 [Dirac fields];
Khriplovich PLB(12)-a1201 [and four-fermion gravitational interaction];
Fresneda et al BJP(15)-a1404 [Maxwell field];
Fabbri et al PRD(14)-a1404,
Fabbri & Vignolo MPLA(16)-a1504 [with Dirac fields];
Fabbri IJGMP(17)-a1611 [Dirac matter fields as particles];
Böhmer et al EPJC(18)-a1709 [mass of gravitating particles].
@ f(T) gravity: Linder PRD(10)-a1005;
Yang EPJC(11)-a1007;
Li et al PRD(11)-a1010 [and local Lorentz invariance];
Yang EPL(11)-a1010 [conformal transformations];
Ferraro & Fiorini PLB(11)-a1103;
Wei et al PLB(12)-a1112 [Noether symmetry];
Tamanini & Böhmer PRD(12)-a1204,
a1304-MG13 [good and bad tetrads];
Nashed AHEP(15)-a1403 [and local Lorentz transformations];
Krššák & Saridakis CQG(16)-a1510 [covariant formulation];
Otalora & Rebouças EPJC(17)-a1705 [causality violations];
Beltrán Jiménez et al a2004 [Minkowski space];
Golovnev & Guzmán a2012 [theoretical foundations];
> s.a. bianchi I models; energy-momentum
pseudotensor; kerr solutions; spherical solutions.
@ f(T) gravity. Hamiltonian: Li et al JHEP(11)-a1105,
Ferraro & Guzmán PRD(18)-a1802 [degrees of freedom];
Blagojević & Nester a2006 [Lorentz invariance].
@ f(R,T) gravity: Carvalho et al EPJC(21)-a2008 [Lagrangian ambiguity].
@ Scalar-torsion theories: Kofinas PRD(15)-a1507 [black holes];
Hohmann et al PRD(18)-a1801 [covariant formulation];
Hohmann PRD(18)-a1801 [general formalism].
@ Cosmology, other: Popławski AR(13)-a1106;
Wanas & Hassan a1209;
Velten & Caramês PRD(17)-a1702 [difficulties of f(R,T) gravity];
Grensing GRG(21)
[coupled to right-handed Majorana neutrinos, dark matter].
@ Other higher-order theories:
Hammond JMP(89),
JMP(90) [second-order equations];
Troncoso & Zanelli CQG(00)ht/99;
Kruglov AFLB(07)-a0710 [quantum];
Capozziello et al CQG(07),
Capozziello & Vignolo AdP(10)-a0910-conf [metric-affine];
Hernaski et al PRD(09)-a0905 [and massive gravitons];
Nikiforova et al PRD(09);
Helayël-Neto et al PRD(10)-a1005 [Einstein-Hilbert-Chern-Simons Lagrangian];
Fabbri & Mannheim PRD(14)-a1405 [continuity of the torsionless limit];
Vasilev et al EPJC(17)-a1706 [stability];
de la Cruz-Dombriz et al PRD(19)-a1812 [infinite-derivative gravity with torsion].
@ Higher-dimensional theories: Mukhopadhyaya et al PRD(02) [large extra dimensions],
PRL(02) [in Randall-Sundrum scenario];
> s.a. kaluza-klein models.
Specific theories:
see conformal, einstein-cartan,
gauge theory, teleparallel,
and unimodular gravity; low-spin
field theories [spin-2 fields].
Related topics:
see action for general relativity; affine connections;
conservation laws; energy conditions;
McVittie Metric; torsion phenomenology.
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