Dirac
Fields in Curved Spacetime| Dirac
Fields in Curved Spacetime |
In General > s.a. quantum
dirac fields; spinors.
* 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-comutative 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]; Huang & Parker PRD(09)-a0811 [Hermiticity
of Hamiltonian, time-dependent metric]; Arminjon & Reifler a0905 [non-uniqueness
problem].
@ History:
Scholz phy/04-in
[Fock & Dirac
1929].
@ 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]; Hijazi et al CMP(01)m.DG/00,
CMP(02)
[with boundary]; 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]; > s.a. observables.
@ Related topics: Cotaescu & Visinescu ht/04-in
[symmetries
and supersymmetries]; Reifler & Morris IJTP(05)-a0706 [Hestenes'
tetrad and spin connections]; Leclerc CQG(06)gq/05 [Hamiltonian
in
non-stationary spacetime]; Arminjon in(07)-a0706 [alternative
form, from
quantum mechanics].
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-in
[Schwarzschild, Kerr, RN];
Doran & Lasenby PRD(02)gq/01 [scattering,
perturbative].
@
Schwarzschild: 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]; Cotaescu MPLA(07)gq [approximate
solution].
@ 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: 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].
@
Kerr-Newman: Page PRD(76); Finster et al CPAM(00)gq/99,
CMP(02);
He & Jing NPB(06)gq [charged,
massive, late-time].
@ Other black hole background: Lyu & Gui IJTP(07)
[Schwarzschild-de Sitter, semi-analytical]; Belgiorno & Cacciatori a0803 [Kerr-Newman-AdS],
JPA(09)-a0807 [Kerr-Newman-de Sitter],
a0810 [charged
de Sitter black holes]; Lyu & Ciu PS(09)
[Reissner-Nordström-de Sitter].
Other Backgrounds > s.a. FRW
spacetime; kantowski-sachs
models;
graphs; huygens'
principle.
@ Constant curvature: Cotaescu MPLA(98)gq,
Takook gq/00-in
[de Sitter space]; Friedrich JGP(00);
Alimohammadi & Vakili AP(04)gq/03;
López-Ortega
GRG(04)
[3D de Sitter]; McMahon et al gq/06/EJP
[Rindler space]; Cotaescu RJP-gq/07 [de Sitter
and AdS]; Crucean MPLA(07)-a0704 [de Sitter];
Bachelot CMP(08)-a0706 [AdS,
well-posedness].
@ Cosmological, FRW models: Villalba & Isasi JMP(02)gq;
Sharif ChJP(02)gq/04;
Zecca IJTP(06);
Finster & Reintjes CQG(09)-a0901 [spatially
closed].
@ Other background: Cotaescu & Visinescu IJMPA(01)
[Taub-NUT]; Groves et al PRD(02)gq [static
spherical, 
Tab
];
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 a0906 [spherically symmetric].
@ With torsion: Zecca IJTP(02); Adak et al IJMPD(03).
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-in;
Arminjon FP(08)gq/07 [two
alternatives]; > s.a. bianchi
models.
@ Einstein-Dirac-(Maxwell): 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].
@ Einstein-Dirac-Yang-Mills: Finster et al MMJ(00)gq/99,
Bernard CQG(06)
[no-black hole result].
main page – abbreviations – journals – comments – other
sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 21
jul
2009