Types of Yang-Mills Gauge Theories  

In General > s.a. gravity; QCD and QCD phenomenology.
* Choice of algebra: Yang-Mills theories can be constructed with "quasiclassical" Lie algebras, a class which contains reductive as well as solvable ones; If we require theories to be ghost-free, then only the standard ones based on compact Lie algebras are allowed, but solvable gauge theories may be relevant for some integrable models based upon the zero-curvature condition.
* U(1): Used to describe electromagnetism and QED (the original one), hypercharge, baryon number, lepton number.
* SU(2): Used to describe isospin.
* SU(2) × U(1): Used in the Weinberg-Salam electroweak theory.
* SU(3): Used to describe QCD, the charge being color.
* SU(5): Used in grand unified theories.
* SO(3,1): Used in attempts to make a gauge theory of gravity.
@ Original theory: Schrödinger ZP(22); Fock ZP(26); London ZP(27); Weyl ZP(29); Pauli RMP(41).
@ U(1) / Abelian theory: Lantsman a1406 [topological Dirac variables, sectors].
@ SU(3): Bolokhov & Faddeev TMP(04) [infrared variables]; Goncharov PLB(05)hp [confinement].
@ Other groups: Baekler et al in(86) [affine group]; Shiraishi IJMPA(92)-a1302 [U(∞) from dimensional reduction of higher-derivative theories]; Nuyts & Wu PRD(03) [non-semisimple]; Lucini & Panero PRP(13) [SU(N), for large N]; Frasca a1705 [SU(N), spectrum, next-to-leading order correction].
@ Non-Abelian theories: Klein in(38); Yang & Mills PR(54) [SU(2)]; Utiyama PR(56) [more general]; Mayer NC(59); Thirring AP(60) [Lorentz group]; Kibble JMP(61); Glashow & Gell-Mann AP(61) [attempt at unification]; Bergmann & Flaherty JMP(78).
@ Chiral: Gambini & Trias PRD(83); Ball PRP(89).
@ With scalar matter: Chopin JHEP(00) [gauge-invariant variables].
@ With Higgs field: Teh IJMPA(01) [axisymmetric solutions]; Matinyan & Ng JPA(03) [partition function and level density].
@ Related topics: Andersson 86 [and cohomology]; Okubo JPA(98) [solvable algebras]; Langmann & Niemi PLB(99)ht [SU(2) and strings]; in Mavromatos & Winstanley CQG(00)ht/99 [SU(∞) and black holes].

Modifications > s.a. Ghost Field; non-commutative field theory; self-dual gauge theories.
@ General references: Wellner AP(81); Chaves ht/98-ch, ht/01-ln; Chaves & Morales ht/99-proc, MPLA(00)ht/99 [grand unification]; Fujii et al IJGMP(06)ht ["universal"]; Bonora & Giaccari a2103 [HS Yang-Mills-like models].
@ With boundary: Sengupta CMP(97); > s.a. gauge theories; poisson structures [Poisson algebra].
@ Massive: 't Hooft NPB(71) [renormalizable model]; Baleanu NCB(03) [Hamilton-Jacobi]; Bettinelli et al PRD(08)-a0705 [from non-linear realizations]; Bettinelli & Ferrari APPB(13)-a1209 [weak-coupling limit]; Yildirim a1412-PhD [topologically massive]; García-Saenz et al JHEP(16)-a1511 [spin-2 partially massless, no-go result].
@ With higher derivatives: Polonyi & Siwek PRD(12)-a1209 [and Higgs field]; Dai a1912 [with matter fields, consistent interactions].
@ Supersymmetric: Brink et al NPB(77); Berkovits & Hull JHEP(98) [D = 10 action]; Ananth et al JPA(20)-a2001 [without anticommuting variables]; > s.a. supersymmetric field theories.
@ Deformed: Finkelstein ht/02 [SU(3)q]; Ünsal & Yaffe PRD(08)-a0803 [double trace deformation]; Cofano et al PRD(15)-a1501; Kotov & Strobl PRD(15)-a1510 [with curved field space]; Santos & Sobreiro EPJC(17)-a1612 [Lorentz-violating].
@ Other modified theories: Baez ht/02 ["Lie 2-groups"]; Strobl PRL(04) [Lie algebroids]; Setare NPB(06) [2D non-local U(N)]; Restuccia & Veiro JPCS(16)-a1412 [octonionic gauge field]; > s.a. born-infeld theory; BRST theory; QCD; string phenomenology; types of gauge theories [higher spin]; unified theories.

Other Dimensionalities and Curved / Discrete Spacetime > s.a. lattice field theory.
@ 0+1 dimensions: Fuster & van Holten JMP(05)ht [SU(2), BRST quantization].
@ 1+1 dimensions: Reinhardt & Schleifenbaum AP(09) [Hamiltonian, Coulomb gauge]; Azuma et al a1207 [on a circle, at finite temperature].
@ 2+1 dimensions: Alimohammadi & Tofighi EPJC(99)ht/98 [on 2D sphere, phase transition]; Karabali et al NPB(00) [with Chern-Simons term]; Diakonov & Petrov PLB(00) [gauge-invariant]; Schulz hp/00; Nair NPPS(02)ht, MPLA(03)ht-in [rev]; Díaz et al PRD(06) [surface invariants]; Agarwal et al NPB(08)-a0705 [coupling to scalar matter]; Fukuma et al JHEP(08), Karabali et al NPB(09)-a0906 [Hamiltonian formalism]; Frasca a1408 [ground state]; Schulz a1605 [note on point-splitting regularization].
@ Higher dimensions: López-Osorio et al PRD(14)-a1402 [compactified]; García-Jiménez et al a1801 [Kaluza-Klein effective description].
@ In curved spacetime: Choquet-Bruhat in(91) [on Lorentzian manifolds]; Sánchez-Monroy & Quimbay AP(12) [1+1, 2+1 and 3+1 dimensional SU(N) theory in anti-de Sitter and Schwarzschild metrics, confining behavior]; Ghanem a1312 [global existence].
@ Discretizations: Castellani & Pagani AP(02)ht/01; Rajeev ht/04-conf [simplicial]; Sushch CUBO(04)mp, CUBO(06)mp [on a complex].
> Theory: see formulations of general relativity; quantum spacetime; spin-foam models.
> Properties and solutions: see cosmological models; fields in schwarzschild spacetime; general relativity solutions with matter.

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