Quantum
Dirac Fields| 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]; Deckert et al a0906 [in an external electrodynamic field].
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
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 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 [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].
> Special features and effects:
see CPT; dirac fields [pilot-wave
model]; Dirac
Hole/Sea; entanglement; quantum
field theory
effects.
Curved Backgrounds > s.a. 4-spinors; 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)
[Reissner-Nordström-Anti-de Sitter].
@ 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 de Sitter]; Sharipov m.DG/06 [massive,
neutral]; Leclerc AP(07)gq/06 [Hamiltonian,
covariant]; Smith CQG(07)
[energy inequalities]; Cianfrani & Montani IJMPA(08)-a0805
[localization and
particles]; Dappiaggi et al a0904 [and
trace anomaly]; > s.a. types
of
quantum
field
theories.
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send feedback and suggestions to bombelli at olemiss.edu – modified 12
aug 2009