Quantization
of Gauge
Theories| Quantization
of Gauge
Theories |
General Considerations > s.a. QED; quantization
of constrained systems; self-dual fields.
* History: Renormalizability was proved by 't Hooft and Veltman; It
works because of dimensional regularization.
* Idea: It is most convenient to work in a gauge-fixed approach, but
then one has to use some method (e.g., BRST charges or Faddeev-Popov ghosts)
to
relate it to gauge invariance; Also, Gribov problem.
Approaches and Techniques > s.a. algebraic
and axiomatic approach; green
functions;
Gupta-Bleuler; vacuum.
* Ambiguities: One ambiguity
is the existence of different theta-sectors.
@ Different variables: Mandelstam PR(68); Haagensen & Johnson NPB(95)
[adapted to Gauss]; > s.a. gauge theories [Wilson
loops].
@ Gauge fixing: Goldstone & Jackiw PLB(78);
Fujikawa & Terashima NPB(00); > s.a.
Gribov Effect.
@ Perturbative: Veltman NPB(68)
[massive Yang-Mills fields]; 't Hooft & Veltman NPB(72)
[Feynman rules and S-matrix].
@ Non-perturbative: Shabanov & Klauder PLB(99)ht [path
integral]; Dzhunushaliev et al hp/04,
hp/04-in
[approximate, n-point functions]; Sobreiro a0705-PhD.
@ Mass: Calixto & Aldaya ht/00-in
[non-Higgs]; Fosco et al JPA(02) [2D, induced by vacuum polarization].
@ Related topics: Halperin AP(95)
[KAM]; Bassetto et al ht/95 [on
a cylinder]; Heitmann PRD(01)
[out of equilibrium]; Kreimer AP(06)
[Hochschild cohomology].
Canonical Quantization > s.a. first-class and second-class
constraints; coherent
states; connection; QED; topological
field theories.
* Approaches: Hamiltonian (Batalin-Fradkin-Vilkovisky), and Lagrangian
(Batalin-Vilkovisky).
@ General references: DeWitt JMP(61),
JMP(62);
Kundt in(66); Gribov NPB(78);
Singer CMP(78);
Friedman & Papastamatiou NPB(83)
[temporal gauge]; Govaerts ht/99-in;
Kanatchikov RPMP(04)ht/03 [precanonical];
Maitra a0804-CMP
[gauge-invariant ground state].
@ Factor ordering: Kuchar PRD(86);
McMullan & Paterson JMP(89),
JMP(89).
@ Quantum configuration space: Ashtekar & Isham CQG(92);
Pause & Heinzl
NPB(98)
[Yang-Mills].
@ Measures on A/G: Ashtekar et al CQG(89)
[2+1 general relativity]; Baez in(94) [1+1 Yang-Mills]; Ashtekar et al in(94)gq,
in(94)ht;
Marolf & Mourão CMP(95)ht/94;
Ashtekar & Lewandowski
JMP(95)gq/94;
Nair & Yelnikov NPB(04)
[3+1]; Levy mp/05 [compact
surface]; Kelnhofer a0707 [on
compact manifolds, and Gribov ambiguity].
@ Batalin-Vilkovisky: Ordóñez et al PLB(93); Dayi IJMPA(96)ht/95.
@ Loop representation: Gambini & Trias PRD(81), LNC(83), PRL(84), NPB(86);
Gambini et al PRD(89);
Loll TMP(92);
Gambini & Setaro NPB(95)
[path representation, with fermions]; Zapata JMP(97)gq;
Ashtekar et al JMP(97)ht/96,
Fleischhack JMP(99)
[2D]; > s.a. lattice gauge theory, Loop
Transform, QCD.
@ Spin networks: Furmanski & Kolawa NPB(87);
Baez AiM(96)gq/94;
Lewandowski & Thiemann CQG(99)gq.
@ Kodama-Chern-Simons state: Mena CQG(95)gq/94 [non-normalizable];
Witten gq/03;
Corichi & Cortez PRD(04)ht/03;
Cartas-Fuentevilla & Tlapanco-Limón PLB(05)ht
[extension]; > s.a. lqg; quantum
gravity phenomenology.
@ Different backgrounds: Lenz et al a0803 [static
spacetimes]
@ Related topics: Odaka ht/95 [inequivalent
quantizations]; Calixto & Aldaya JPA(99)ht [group
quantization]; Driver & Hall CMP(99)
[Segal-Bargmann transform]; Muslih et al
IJTP(00)
[massive]; Larsson
ht/05 [manifestly
covariant]; Freidel et al PLB(06)
[solution, 3+1].
Specific Concepts, Effects,Theories > s.a.
gravitation; Proca
Theory; QCD [including
confinement]; QED; topological
field theories.
@ Matter couplings: Gies & Hammerling PRD(05)ht [in
world-line, loop space approach].
@ Spectrum, 2+1: Leigh
et al PRL(06)ht/05, PRD(07)ht/06, a0704-in;
Brits JHEP(07); Freidel
et al a0801-in
[and 3+1].
@ Lower-dimensional: Oeckl JPA(08)ht/06 [2D
Yang-Mills, with corners].
@ Related topics: Dzhunushaliev & Singleton IJTP(99)
[spherically symmetric SU(3)]; > s.a. path
integral.
> Related topics: see Higgs
Mechanism; phase transition; quantum
chaos
General References > s.a. BRST; quantum
field theory and algebraic
approach; stochastic quantum mechanics;
regularization.
@ Textbooks and reviews: Faddeev & Slavnov 80; Jackiw RMP(80);
Mayer APA(81); Nakanishi & Ojima 90; Henneaux & Teitelboim 92; Makeenko
02.
@ Simple: Holstein AJP(88).
@ Renormalization: 't Hooft
ht/94-ln;
Cheng & Li
IJMPA(98)
[Dyson's program]; Dine & Gray PLB(00)ht/99 [non-renormalization
theorems]; Kawamoto & Matsuo
ht/03; Hollands
a0705 [consistent,
in curved spacetime]; > s.a. renormalization
group.
@ Boundary conditions: Actor PhyA(90).
@ Related topics: Manoukian PRD(86);
Villanueva
et al JPA(00)ht/99 [use
gauge-invariant states]; > s.a. effective field theories.
Variations, Generalizations > s.a. non-commutative
field theories;
types of quantum field theories [deformed].
@ Antibracket formalism: Witten MPLA(90).
@ Non-local: Kleppe & Woodard NPB(92);
Amorim & Barcelos-Neto
JMP(99)ht [massive,
canonical vs path integral].
@ Other variations: Reisenberger gq/94-in
[world-sheet]; Lahiri PRD(01)
[2-form, renormalizability]; Biró et al FPL(01)ht [from
higher-dimensional classical theory]; Álvarez-Gaumé & Wadia
PLB(01)
[on quantum phase space]; Bertrand a0704 [topologically
massive, canonical].
Main page – Abbreviations – Journals – Comments – Other
sites – Acknowledgements
Send feedback and suggestions to bombelli at olemiss.edu – Modified
21 jun 2008