Quantum Dirac Fields |
Canonical Quantization
* Creation / annihilation operators:
Use as variables to quantize the coefficients of the expansion
ψ = ∑s ∑k (bk,s uk,s + dk,s† vk,s) ,
with {uk,s, vk,s} a complete orthonormal set of solutions; They satisfy
{bk,s, bk',s'†} = {dk,s, dk',s'†} = δkk' δss' .
* Scalar product:
(φ, ψ):= ∫Σ dn−1x φ* γ0 ψ = ∫Σ dn−1x φ†ψ .
@ References: Jing PRD(05) [finite V, Dirac vs reduced phase space]; Deckert et al JMP(10)-a0906 [in an external electrodynamic field]; Kaźmierczak a1010, a1011 [quantization without using Poincaré symmetry]; Bennett AP(14) [first-quantized electrodynamics].
Other Approaches and Features
> s.a. QED; feynman propagator;
green functions; path integrals.
* Foldy-Wouthuysen representation:
A representation of the Dirac matrices that does not connect positive with negative
energy states; The position operator x differs from that in the usual Dirac
representation by a unitary similarity transformation.
@ Foldy-Wouthuysen:
Foldy & Wouthuysen PR(50);
Schweber 61;
Jehle & Parke PR(65);
Silenko PPNL(08)mp/06,
Neznamov a0804,
Neznamov & Silenko JMP(09)-a0906 [relationship with Dirac representation].
@ Path integral: Nakamura JMP(97),
JMP(00) [measure];
Gosselin & Polonyi AP(98);
Alexandrou et al PRA(99)ht/98 [massive];
Polonyi PLB(99)ht/98-conf;
Fosco et al AP(08) [2+1 dimensions];
> s.a. path integrals for quantum feld theory.
@ Semiclassical limit: Bolte & Keppeler PRL(98)qp,
AP(99)qp/98 [time-evolution kernel, trace formula];
> s.a. Zitterbewegung.
@ Special states:
Vollick PRD(98) [E < 0];
Solomon CEJP(06)ht/04 [Maxwell-Dirac, spacelike energy-momentum];
Campos et al PRA(14)-a1402 [non-classical states with positive Wigner function].
@ And other fields: Aste EPJC(14)-a1307 [derivative coupling to a massless scalar field].
@ Related topics:
García-Chung & Morales-Técotl PRD(14) [polymer quantization];
Manning a1512 [in rotating reference frames];
Kim JHEP(17)-a1706 [entanglement, Rényi entropies, computations].
> Special features and effects:
see CPT theorem; dirac fields [pilot-wave model];
Dirac Hole/Sea; entanglement;
quantum field theory effects.
Curved Backgrounds > s.a. quantum field theory
effects in curved spacetime and in different curved backgrounds.
@ General references: Leclerc AP(07)gq/06 [Hamiltonian, covariant];
Hack PhD(10)-a1008 [backreaction];
Gosselin & Mohrbach EPJC(11)-a1009 [semiclassical approximation, effective couplings];
Obukhov et al PRD(11)-a1106 [in strong gravitational fields];
Cortez et al PRD(17)-a1608 [2+1 dimensions].
@ Energy inequality: Fewster & Verch CMP(02);
Dawson & Fewster CQG(06)gq [explicit bound].
@ Black hole: Bolashenko & Frolov TMP(89);
Singh PRD(05)gq/04 [spin and chiral dynamics];
Belgiorno & Cacciatori CQG(08) [Reissner-Nordström-Anti-de Sitter];
Casals et al PRD(13)-a1207 [Kerr solutions];
Winstanley a1310-proc
[massless fermion field on a non-extremal Kerr black hole].
@ FLRW backgrounds:
Montaldi & Zecca IJTP(94) [neutrinos],
IJTP(98) [normal modes];
Cortez et al PRD(15)-a1509,
PRD(16)-a1603 [preferred Fock quantization];
Cortez et al AP(17)-a1609,
AMP(18)-a1803 [uniqueness of Fock quantization];
Machado et al PRD(18)-a1811 [electron-positron pairs];
> s.a. fields in FLRW spacetimes.
@ Other backgrounds:
Oriti NCB-gq/99-proc, gq/00/CQG [Rindler space; Unruh effect];
Jin CQG(00) [static];
Havare et al NPB(04)
[de Sitter, particle creation];
> s.a. fields in de Sitter space.
@ Obstructions: Carey & Mickelsson LMP(00) [odd-dimensional manifold with boundary].
@ Related topics: Sharipov m.DG/06 [massive, neutral];
Smith CQG(07) [energy inequalities];
Cianfrani & Montani IJMPA(08)-a0805 [localization and particles];
Dappiaggi et al RVMP(09)-a0904 [and trace anomaly];
Müller a1002 [Wick rotation];
Sanders RVMP(10) [as a locally covariant quantum field theory];
> s.a. 4-spinors; deformation quantization;
field theory in non-commutative spacetime; types of quantum
field theories.
main page
– abbreviations
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– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 17 jan 2021