Gauge Theories of the Yang-Mills Type  

In General > s.a. gauge theory; Wilson Loop.
* Idea: Gauge theories with a specific form for the action/equations of motion; The original type of gauge theory, and still the most widely used one.
* Evidence: First direct evidence with the 1973 discovery of flavor-changing neutral currents at CERN.

Classical Dynamics > s.a. gauge theory; lattice gauge theory.
* Action: In terms of the curvature Fab of the Lie algebra-valued connection Aa ("tr" uses the metric on G),

S[A] = M dv gab gmn tr(Fam Fbn) = # M tr(F *F).

* Field equations: They are the source equations, and

DF:= dF + [A, F] = 0 ,      D*F = J ;

the first one is the Bianchi identity, and the second is conformally invariant (masslessness; J is the source current).
* Matter fields: The coupling of the gauge field to matter is usually taken to be minimal; The free term "FF" is added to the matter Lagrangian, and all derivatiives of matter fields are replaced by gauge-covariant derivatives D.
@ Action: Aldrovandi & Pereira RPMP(88) [lagrangians]; & Sengupta; Fine JMP(00)m.DG [lower bound on a Riemann surface]; Tolksdorf JGP(07) [form linear in the curvature].

Hamiltonian Formulation and Evolution > s.a. solutions [singularities]; types of yang-mills theories [1+1 dimensions].
* Hamiltonian / Energy:

H(A, E) = d3x tr(E2 + B2) = # dv gab gmn tr(Fam Fbn) .

@ General references: Cronstrom ht/98, ht/99; Sniatycky RPMP(99); Ozaki ht/00/PRD [QCD]; Vignolo et al IJGMP(05)mp; Reinhardt et al a0807-in [Coulomb gauge]; Gerhardt a0908 [energy gap].
@ Gauge-invariant variables: Lunev TMP(93) [and Yang-Mills-Higgs]; Freidel ht/06.
@ Cauchy problem: Segal JFA(79); Eardley & Moncrief CMP(82), CMP(82).
@ With matter: Lusanna IJMPA(95), IJMPA(95) [fermions].
@ Structure of configuration space: Fuchs et al NPB(94); Fuchs ht/95-in; Rajeev & Rossi JMP(96) [on a cylinder]; Pause & Heinzl NPB(98)ht; Nair & Yelnikov NPB(04)ht/03 [measure]; Agarwal & Nair NPB(09) [on R S2].

Chaos > s.a. quantum chaos.
@ General references: Baseyna et al JETP(79); Matinyan et al JETP(81); Chirikov & Shepelyanskii JETP(81), SJNP(82); Kawabe & Ohta PRD(90), PRD(91); Kawabe PLB(92); Wellner PRL(92); Biró et al 95; Kawabe & Ohta PLB(94); Nielsen et al cd/96, cd/96-in; Salasnich MPLA(97)qp [quantum]; Casetti et al JPA(99)cd/98 [U(1) lattice gauge theory]; Biró et al NPPS(00)hp/99; Bambah et al ht/02-in.
@ Integrability: Witten JGP(92); Inami et al NPB(06)ht [non-integrability of self-dual Yang-Mills-Higgs]; > s.a. self-dual solutions.

Other Issues and Effects > s.a. boundaries; duality; entropy bounds; gauge theory solutions; QCD [confinement].
* Gauge choice: See Axial, Coulomb, Lorenz gauge.
* Mass generation: A possible mechanism is through a topological coupling of vector and tensor fields; After integrating over the tensor degrees of freedom, one arrives at an effective massive theory that is gauge invariant but non-local.
@ Mass generation: Flores-Baez et al IJMPA(06) [without Higgs]; Sorella AP(06)-a0704.
@ Related topics: DeGrand et al NPB(98) [SU(2), topological susceptibility]; Edwards et al PLB(98) [fractional topological charge]; Gambini et al PRD(99)gq/98 [Immirzi-like parameter]; Bizon & Tabor PRD(01) [singularities and critical phenomena].
> Other effects: see Higgs Mechanism; thermodynamics; theta sectors.

References > s.a. [gauge theory]; BRST; history of physics; lattice gauge theory; QCD; string phenomenology.
@ Articles, I: 't Hooft SA(80)jun; Wilczek PW(89)feb; Barlow EJP(90).
@ Books, II: Aitchison & Hey 04.
@ Books and reviews: Abers & Lee PRP(73); Coleman in(75); Iliopoulos pr(76); Mayer 77; Yang NYAS(77); O'Raifeartaigh RPP(79); Bleecker 81; Gaillard & Stora ed-83; Quigg 83; Chaichian & Nelipa 84; Cheng & Li 84; Bailin & Love 86; O'Raifeartaigh 86; Carmeli et al 89; Mills AJP(89)jun; Huang 91; Cheng & Li 00 [problems]; Frampton 00; Pokorski 00; 't Hooft ed-05.
@ As perturbed topological field theory: Cattaneo et al CMP(98) [deformed BF theory]; Kondo PRD(98)ht, IJMPA(01); Rovelli & Speziale GRG(07)gq/05 [equivalent to perturbed abelian theory].
@ Reformulations: Faddeev & Niemi PRL(99)ht/98 [partially dual variables]; Majumdar & Sharatchandra PLB(00)ht [as ADM-type theory of metrics]; Cianci et al JPA(03), add JPA(04) [geometrical]; Sevostyanov mp/04-wd [as integrable, near ground state]; Carta et al AdP(06)ht/05 [Koopman-von Neumann formulation]; Gorsky & Rosly JHEP(06)ht/05 [light-cone formalism]; Catren & Devoto CMP(08)-a0710 [extended connection]; Maraner & Pachos PLA(09) [from fermionic lattice models]; > s.a. gauge theory [variables], sheaf.

Other Topics > s.a. connections; conservation laws; solutions [space of solutions]; types of yang-mills theories.
@ General references: Sniatycki RPMP(88) [charges]; Wald in(88); Henneaux & Teitelboim PLB(90); Henneaux et al NPB(90); Sniatycki CMP(91); Shabanov PLB(01)ht [infrared limit]; Capri et al PRD(05)ht [non-local mass operator]; Marateck a0712 [rederivation]; Catren SHPMP(08) [geometric foundations].
@ Gauge-invariant calculations: Arnone et al PRD(03)ht/02; Rosten JPA(06)ht/05; > s.a. renormalization.
@ Symmetries: Marchildon JGTP(95)mp/03 [Lie symmetries]; Torre JMP(95); Pons et al JMP(00)gq/99 [Einstein-Yang-Mills]; Pohjanpelto DG&A(04) [local, semi-simple, classification]; > s.a. solutions.

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