Dirac Fields in Curved Spacetime| Dirac Fields in Curved Spacetime |
In General > s.a. quantum dirac fields; spinors;
neutrinos; types of field theories [alternatives to Dirac theory].
* Result: There are no static
or time-periodic solutions on a Reissner-Nordström background.
* Coupling: The spin current
of the Dirac field couples to torsion or (as in general relativity) to the
tetrad anholonomy.
* Operator and eigenvalues:
The fact that most of the geometric information of a compact riemannian
spin manifold M is encoded in its Dirac operator D has
become one of the building blocks of non-commutative geometry;
> s.a. spectral and
non-commutative geometry.
@ General references: Rudiger PRS(81)
[and WKB derivation of spinning particle equation of motion];
Sen JMP(81) [for neutrinos];
in Birrell & Davies 84;
Bigazzi & Lusanna IJMPA(99)ht/98 [spacelike hypersurfaces];
Cardoso CQG(06) [two-component, wave equation];
Nyambuya EJTP(07)-a0709 [and anomalous magnetic moment],
a0711/EJTP,
FP(08) [new proposed forms];
Cartoaje a1006 [coordinate-free notation];
Alhaidari & Jellal PLA(15)-a1106 [without spin connections or vierbeins];
Obukhov et al PRD(13)-a1308,
comment Arminjon a1312;
Gies & Lippoldt PRD(14) [with local spin-base invariance];
Collas & Klein a1809-ln;
Struckmeier et al a1812 [effective mass term].
@ History:
Scholz phy/04-proc [Fock & Dirac 1929];
Kay GRG(20)-a1906 [on Schrödinger's 1932 paper].
@ Hamiltonian: Leclerc CQG(06)gq/05 [Hamiltonian in non-stationary spacetime];
Huang & Parker PRD(09)-a0811 [Hermiticity, time-dependent metric].
@ Hamiltonian, non-uniqueness problem:
Arminjon & Reifler AdP(11)-a0905,
JPCS(10)-a1001;
Arminjon AdP(11)-a1107,
IJGMP(13)-a1205 [solution of the non-uniqueness problem];
Gorbatenko & Neznamov a1301 [no problem];
Arminjon IJTP(13)-a1302 [spin-rotation coupling],
JPCS(15)-a1502.
@ Operator and eigenvalues: Trautman APPB(95)ht/98 [non-orientable surface];
Landi & Rovelli PRL(97)gq/96;
Esposito 98-ht/97 [spectral geometry];
Adam et al PRD(99)ht,
PLB(00)ht/99 [3D, + abelian gauge theory, zero modes];
Agricola & Friedrich JGP(99);
Kraus JGP(00) [on Sn];
Ammann & Bär JGP(00) [and curvature];
Cnops 02 [intro];
Ammann JGP(04)
[T2 with non-trivial spin structure];
Jung et al JGP(04) [on a Riemannian foliation];
Avramidi IJGMP(05)mp [including matrix geometry];
Alexandrov JGP(07) [locally reducible Riemannian manifolds];
Goette CMP(07) [compact symmetric space];
Dąbrowski & Dossena CQG(13)-a1209 [and diffeomorphisms];
Asorey et al IJGMP(15)-a1510 [topology and geometry of self-adjoint and elliptic boundary conditions];
> s.a. observables.
@ With boundaries: Hijazi et al CMP(01)m.DG/00,
CMP(02);
Govindarajan & Tibrewala PRD(15)-a1506 [edge states];
Große & Murro a1806 [globally hyperbolic manifolds with timelike boundary].
@ Related topics:
Cotăescu & Visinescu in(07)ht/04 [symmetries and supersymmetries];
Reifler & Morris IJTP(05)-a0706 [Hestenes' tetrad and spin connections];
Arminjon in(07)-a0706 [alternative form, from quantum mechanics];
Arminjon & Reifler IJGMP(12)-a1012 [four-vector vs four-scalar representations],
BJP(13)-a1103 [generalized de Broglie relations],
JGSP-a1109-talk
[classical-quantum correspondence and wave-packet solutions];
Cariglia a1209-proc [hidden symmetries];
Vassiliev MG14(17)-a1512 [non-geometric representation].
On a Black Hole Background > s.a. black-hole
uniqueness; schwarzschild-de sitter spacetime.
@ General references:
Radford & Klotz JPA(79),
JPA(79);
Cohen & Powers CMP(82);
Goncharov PLB(99)gq [twisted, Schwarzschild and Reissner-Nordström];
Mukhopadhyay gq/01-MG9
[Schwarzschild, Kerr, Reissner-Nordström spacetimes];
Doran & Lasenby PRD(02)gq/01 [scattering, perturbative].
@ Schwarzschild spacetime: Jin CQG(98)gq/00 [scattering theory];
Mukhopadhyay & Chakrabarti CQG(99)gq;
Carlson et al PRL(03)gq
[numerical Tab];
Jing PRD(04)gq [late-time];
Doran et al PRD(05)gq [particle absorption];
Cáceres & Doran PRA(05) [energy spectrum];
Cho & Lin CQG(05),
Dolan et al PRD(06) [massive, scattering];
Cotăescu MPLA(07)gq [approximate solution];
Smoller & Xie AHP(12)-a1104 [massless Dirac fields].
@ Reissner-Nordström: Finster et al JMP(00)gq/98;
Belgiorno PRD(98) [massive];
Melnyk CQG(00) [charged];
Mukhopadhyay CQG(00)gq;
Jing PRD(05)gq/04 [late-time].
@ Kerr spacetime:
Unruh PRL(73);
Mukhopadhyay IJP(99)gq;
Mashhoon CQG(00)gq [spin couplings];
Chakrabarti & Mukhopadhyay MNRAS(00)ap,
NCB(00);
Mukhopadhyay & Chakrabarti NPB(00)gq;
Batic JMP(07)gq/06 [scattering];
Dolan & Dempsey CQG(15)-a1504 [bound states];
Röken a1507
[separability in advanced Eddington-Finkelstein-type coordinates].
@ Kerr-Newman:
Page PRD(76);
Finster et al CPAM(00)gq/99,
CMP(02);
He & Jing NPB(06)gq [charged, massive, late-time];
Dariescu et al a2102.
@ Other black hole background: Lyu & Gui IJTP(07) [Schwarzschild-de Sitter, semi-analytical];
Belgiorno & Cacciatori JMP(10)-a0803 [Kerr-Newman-AdS],
JPA(09)-a0807 [Kerr-Newman-de Sitter],
PRD(09)-a0810 [charged de Sitter black holes];
Lyu & Ciu PS(09) [Reissner-Nordström-de Sitter];
Sánchez et al PLB(11)-a1110 [massive neutrinos in a SdS black hole];
Cebeci & Özdemir CQG(13)-a1212 [Kerr-Taub-NUT spacetime];
Farooqui a1508 [Kerr, spin precession].
Other Backgrounds > s.a. kantowski-sachs models;
graphs; huygens' principle.
@ Constant curvature: Cotăescu MPLA(98)gq,
Takook gq/00-proc [de Sitter space];
Friedrich JGP(00);
Alimohammadi & Vakili AP(04)gq/03;
López-Ortega GRG(04) [3D de Sitter];
McMahon et al gq/06 [Rindler space];
Cotăescu RJP(07)gq [de Sitter and AdS];
Crucean MPLA(07)-a0704 [de Sitter];
Bachelot CMP(08)-a0706 [AdS, well-posedness];
Kanno et al JHEP(17)-a1612 [de Sitter space];
Santos & Barros IJGMP(19)-a1704 [Rindler space].
@ Cosmological, FLRW models: Villalba & Isasi JMP(02)gq;
Sharif ChJP(02)gq/04;
Zecca IJTP(06);
Finster & Reintjes CQG(09)-a0901 [spatially closed];
Dhungel & Khanal ChJP(13)-a1109;
Yagdjian AP(20)-a2006 [fundamental solutions];
> s.a. FLRW spacetime.
@ Other background:
Cotăescu & Visinescu IJMPA(01) [Taub-NUT];
Groves et al PRD(02)gq
[static spherical, \(\langle\)Tab\(\rangle\)];
Cariglia CQG(04)ht/03 [with Yano tensors];
Talebaoui GRG(05) [plane wave];
Fernandes et al gq/07 [vacuumless defects];
Al-Badawi & Sakalli JMP(08)
[rotating Bertotti-Robinson spacetime];
López-Ortega LAJPE(09)-a0906 [spherically symmetric];
Faba & Sabín PRD(19)-a1901 [exotic spacetimes];
> s.a. deformed uncertainty relations [in graphene].
@ With non-trivial topology:
Gózdz PRD(10);
Jackiw PS(12)-a1104-talk [zero-energy modes];
Cuenin a1311 [on the half-line].
@ With torsion: Zecca IJTP(02);
Adak et al IJMPD(03);
Formiga & Romero IJGMP(13)-a1210 [and non-metricity];
> s.a. Immirzi Parameter.
Coupled to Gravity > s.a. canonical general
relativity; spinning particles [derivation of coupling].
@ General references:
Brill & Wheeler RMP(57);
Dirac in(62);
Brill & Cohen JMP(66);
Finster et al PRD(99)gq/98 [particle-like];
Saaty mp/01;
Aldrovandi et al gq/04-fs;
Arminjon FP(08)gq/07 [two alternatives];
Chafin a1403
[Dirac matrices as dynamical fields];
Singh a1705
[Compton-Schwarzschild length and modified Einstein-Cartan-Dirac equations];
> s.a. bianchi models.
@ Einstein-Dirac-(Maxwell) theory:
Finster et al PLA(99)gq/98 [particle-like],
CMP(99)gq/98,
MAA(01)gq/99 [no-black-hole result],
MPLA(99)gq [soliton-like];
Zecca IJTP(03) [with torsion];
Ranganathan gq/03 [Kerr-Newman-like];
Mei PLB(11)-a1102 [solution representing a massive fermion].
@ Einstein-Dirac-Yang-Mills theory: Finster et al MMJ(00)gq/99,
Bernard CQG(06) [no-black hole result].
@ Other theories: Adak CQG(12)-a1107
[in the Poincaré gauge theory of gravity with torsion and curvature];
Sert & Adak GRG(13) [topologically massive gravity].
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