Quantization of Gauge Theories |
In General
> s.a. QCD; 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.
@ Textbooks and reviews: Faddeev & Slavnov 80;
Jackiw RMP(80);
Mayer APA(81);
Nakanishi & Ojima 90;
Henneaux & Teitelboim 92;
Makeenko 02;
Witten a0812-ln [overview];
Prokhorov & Shabanov 11;
Zeidler 11;
Cline a2005-ln.
@ General references: Holstein AJP(88)may;
Frasca EPJP(17)-a1509 [2-point function];
Milsted & Osborne PRD(18)-a1604 [quantum-information perspective].
@ Renormalization:
't Hooft ht/94-ln;
Cheng & Li IJMPA(98) [Dyson's program];
Dine & Gray PLB(00)ht/99 [non-renormalization theorems];
Kawamoto & Matsuo PTP(08)ht/03;
Hollands RVMP(08)-a0705 [consistent, in curved spacetime];
Tupper a1412
[unitarity and renormalizability in a single framework];
> s.a. renormalization group.
@ With boundaries:
Actor PhyA(90) [boundary conditions];
Cattaneo et al CMP(18)-a1507 [perturbative BF-BFV quantization scheme];
Díaz-Marín & Oeckl Sigma(18)-a1712 [using general boundary quantum field theory].
@ Related topics: Manoukian PRD(86);
Villanueva et al JPA(00)ht/99 [use gauge-invariant states];
> s.a. effective field theories.
> Related topics: see BRST quantization;
quantum field theory and algebraic approach; stochastic
quantum mechanics; regularization.
Approaches and Techniques > s.a. algebraic and axiomatic
approach; Faddeev-Jackiw Method; green functions;
Gupta-Bleuler; lqg; 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);
Slavnov TMP(09)-a0902 [avoiding the Gribov problem];
Ghorbani & Esposito IJGMP(11)-a1009,
Slavnov a1503/TMP [Slavnov formulation, rev];
> s.a. Gribov Effect.
@ Perturbative:
Veltman NPB(68) [massive Yang-Mills fields];
't Hooft & Veltman NPB(72) [Feynman rules and S-matrix];
Schubert a1410-th [multi-loop scattering amplitudes];
Anselmi JHEP(19)-a1909 [proof of perturbative unitarity];
> s.a. scattering amplitudes.
@ Non-perturbative:
Shabanov & Klauder PLB(99)ht [path integral];
Dzhunushaliev et al hp/04,
AIP(05)hp/04 [approximate, n-point functions];
Sobreiro PhD(07)-a0705;
Chatterjee PhD-a1104 [dual confinement of magnetic monopoles];
> s.a. holonomies [holonomy algebras].
@ Mass: Calixto & Aldaya NPPS(00)ht [non-Higgs mechanism];
Fosco et al JPA(02) [2D, induced by vacuum polarization];
Faddeev a0911-fs.
@ 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];
Dietrich PRD(09)-a0904 [fluctuations around classical configurations];
Schroer FP(11)-a1012;
Binosi & Quadri PRD(12)-a1203 [background-field method];
Kreimer et al AP(13)-a1208 [graph polynomials and graph cohomology];
Aastrup & Grimstrup a2008 [from metric structure on space of connections].
Canonical Quantization > s.a. first-class
and second-class constraints; 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-conf;
Kanatchikov RPMP(04)ht/03 [precanonical];
Bracken MPLA(09) [Dirac brackets];
Kanatchikov RPMP(18)-a1805 [precanonical].
@ Factor ordering: Kuchař 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 JMP(08)-a0707 [on compact manifolds, and Gribov ambiguity].
@ Batalin-Vilkovisky:
Ordóñez et al PLB(93);
Dayi IJMPA(96)ht/95;
Reshetnyak a1412-proc [without Gribov copies].
@ 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.
@ Other states: Maitra a0804/CMP [gauge-invariant ground state];
Boulton et al a1708 [bound states in YM-Higgs theory];
> s.a. coherent states.
@ Different backgrounds: Lenz et al PRD(08)-a0803 [static spacetimes];
Hollands RVMP(08)-a0705 [renormalized, in curved spacetime]
@ 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 dimensions: Leigh et al PRL(06)ht/05,
PRD(07)ht/06,
CJP(07)-a0704-proc;
Brits JHEP(07);
Freidel et al a0801-proc,
Frasca a1708-proc
[and 3+1, solution of Schwinger-Dyson equations].
@ 2D Yang-Mills theory: Oeckl JPA(08)ht/06 [with corners];
Nguyen a1508
[perturbation theory vs the full quantum theory];
Brothier & Stottmeister a1907 [operator-algebraic approach].
@ Types of theories:
Dzhunushaliev & Singleton IJTP(99) [spherically symmetric SU(3)];
Wiesendanger PRD(09)-a0903,
JModP(14)-a1308 [volume-preserving diffeomorphisms, and proof of renormalizability];
> s.a. path-integral quantization.
> Related topics: see Asymptotic
Freedom; higgs mechanism; phase transitions;
quantum chaos; thermodynamic systems.
Variations, Generalizations > s.a. non-commutative field theories;
types of quantum field theories [deformed].
@ Antibracket formalism: Witten MPLA(90).
@ Higher-spin fields: Wagenaar & Rijken PRD(09)-a0905;
Schroer a1410 [Hilbert-space setting].
@ Non-local: Kleppe & Woodard NPB(92);
Amorim & Barcelos-Neto JMP(99)ht [massive, canonical vs path integral].
@ Other variations:
Reisenberger gq/94-MG7 [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 & Govaerts JPA(07)-a0704 [topologically massive, canonical];
Pedro a1911.
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