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 φψ .

@ 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 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 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 [uniqueness of Fock quantization]; > s.a. fields in FLRW spacetimes.
@ Other backgrounds: Oriti gq/00/CQG [Rindler space; Unruh effect]; Jin CQG(00) [static]; Havare et al NPB(04) [de Sitter space, particle creation];
@ 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.


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