Quantum Dirac Fields  

Canonical Quantization
* Creation/annihilation operators: Use as variables to quantize the coefficients of the expansion

= 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'} = kk' ss' .

* Scalar product:

(,):= Sigma dn–1x * 0 = Sigma dn–1x .

@ References: Jing PRD(05) [finite V, Dirac vs reduced phase space].

Other Approaches and Features > s.a. 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 mp/06, Neznamov a0804 [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 ht/98-in, PLB(99); Fosco et al AP(08) [2+1]; > s.a. path integrals for quantum feld theory.
@ Semiclassical limit: Bolte & Keppeler PRL(98)qp, AP(99)qp/98 [t-evolution kernel, trace formula]; > s.a. Zitterbewegung.
@ Special states: Vollick PRD(98) [E < 0]; Solomon CEJP(06)ht/04 [Maxwell-Dirac, spacelike energy-momentum].
> Special features and effects: see CPT; dirac fields [pilot wave model]; Dirac Hole/Sea; entanglement; quantum field theory effects.

Curved Backgrounds > s.a. quantum field theory effects in curved spacetime.
@ 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) [RN-AdS].
@ Robertson-Walker: Montaldi & Zecca IJTP(94) [neutrinos], IJTP(98) [normal modes]; > s.a. FRW spacetimes.
@ Obstructions: Carey & Mickelsson LMP(00) [odd-dimensional manifold with boundary].
@ Related topics: Oriti gq/00/CQG [Rindler; Unruh effect]; Jin CQG(00) [static spacetime]; Havare et al NPB(04) [particle creation in dS]; Sharipov m.DG/06 [massive, neutral]; Leclerc AP(07)gq/06 [Hamiltonian, covariant]; Smith CQG(07) [energy inequalities]; Cianfrani & Montani a0805-IJMPA [localization and particles].


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