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.
@ 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].
@ SU(3): Bolokhov & Faddeev TMP(04) [infrared variables]; Goncharov PLB(05)hp [confinement].
@ Other groups: Baekler et al in(86) [affine group]; Nuyts & Wu PRD(03) [non-semisimple].
@ Related topics: SAnderson 86 [and cohomology]; Choquet-Bruhat in(91) [on Lorentzian manifolds]; 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. born-infeld; non-commutative field theory; self-dual; types of gauge theories.
@ General references: Wellner AP(81); Chaves ht/98-in, ht/01-in; Chaves & Morales ht/99-in, MPLA(00)ht/99 [grand unification]; Baez ht/02 ["Lie 2-groups"]; Strobl PRL(04) [Lie algebroids]; Fujii et al IJGMP(06)ht ["universal"].
@ Massive: 't Hooft NPB(71) [renormalizable model]; Baleanu NCB(03) [Hamilton-Jacobi]; Bettinelli et al a0705 [from non-linear realizations].
@ Supersymmetric: Berkovits & Hull JHEP(98) [D = 10 action]; > s.a. supersymmetric field theories.
@ Deformed: Finkelstein ht/02 [SU(3)_q]; Unsal & Yaffe a0803 [double trace deformation].
@ Other theories: Setare NPB(06) [2D non-local U(N)].

References > s.a. BRST; lattice field theory; QCD; string phenomenology; unified theories.
@ Original theory: Schrödinger ZP(22); Fock ZP(26); London ZP(27); Weyl ZP(29); Pauli RMP(41).
@ Non-Abelian theories: O 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).
@ With boundary: Sengupta CMP(97); > s.a. gauge theories.
@ 0+1 dimensions: Fuster & van Holten JMP(05)ht [SU(2), BRST quantization].
@ 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-in, ht/03-in [rev]; Díaz et al PRD(06) [surface invariants]; Agarwal et al a0705 [coupling to scalar matter]; Fukuma et al JHEP(08) [Hamltonian formalism].
@ Discretizations: Castellani & Pagani AP(02)ht/01; Rajeev ht/04-in [simplicial]; Sushch CUBO(04)mp, CUBO(06)mp.

And Gravity > see cosmological models; formulations of general relativity; quantum spacetime; solutions of general relativity [with matter]; spin foam.

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