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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