Types of Yang-Mills Gauge Theories| 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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