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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