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: The first direct evidence came with the 1973 discovery of flavor-changing neutral currents at CERN.

Classical Dynamics > s.a. Faddeev-Niemi Equations; gauge theory [including loop-based variables]; lattice gauge theory; twistors.
* Action: In terms of the curvature Fab of the Lie algebra-valued connection Aa ("tr" uses the metric on G),

S[A] = \(1\over2\)M dv gab gmn tr(Fam Fbn) = # M tr(F ∧ *F).

* Field equations: They are the source equations, and

\(DF:= {\rm d}F + [A, F] = 0\;,\qquad D^*F = J\) ;

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 derivatives ∇ of matter fields are replaced by gauge-covariant derivatives D.
@ General references: Boozer AJP(11)sep [coupled particle-field system, 2D].
@ Action: Aldrovandi & Pereira RPMP(88) [existence of Lagrangians]; & Sengupta; Fine JMP(00)m.DG [lower bound on a Riemann surface]; Tolksdorf JGP(07) [form linear in the curvature]; Escalante & Berra IJPAM-a1301 [as a constrained BF-like theory]; Brandt et al AP(19)-a1810 [first-order, in background field].

Hamiltonian Formulation and Evolution > s.a. hamiltonian systems; 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; Śniatycki RPMP(99); Ozaki IJMPA(01)ht/00 [QCD]; Vignolo et al IJGMP(05)mp; Reinhardt et al a0807-conf, PoS-a0911 [Coulomb gauge]; Gerhardt CMP(10)-a0908 [energy gap]; Prokhorov & Shabanov 11; Balachandran et al MPLA(17)-a1704 [equations of motion as constraints].
@ Gauge-invariant variables: Lunev TMP(93) [and Yang-Mills-Higgs]; Freidel ht/06; Guo AP(16)-a1410 [metric-like variables].
@ 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-conf; Rajeev & Rossi JMP(96) [on a cylinder]; Pause & Heinzl NPB(98)ht; Nair & Yelnikov NPB(04)ht/03 [measure]; Agarwal & Nair NPB(09) [on \(\mathbb R\) × S2].

Other Issues and Effects > s.a. chaos in field theories; 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; Savvidy PLB(10)-a1001 [topological]; Frasca a1007 [and supersymmetry].
@ 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]; Bizoń & Tabor PRD(01) [singularities and critical phenomena]; Fischer et al AP(09) [infrared behavior, Landau gauge].
> Other effects: see higgs mechanism; Memory Effects; thermodynamics; theta sectors.
> Related topics: see boundaries; duality; entropy bounds; Makeenko-Migdal Equation.

References > s.a. gauge theory / BRST; history of physics; lattice gauge theory; QCD [including finite-temperature theory]; string phenomenology.
@ Articles, I: 't Hooft SA(80)jun; Wilczek PW(89)feb; Barlow EJP(90).
@ Books, II: Aitchison & Hey 12.
@ 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; Chaichian & Nelipa 84; Cheng & Li 84; Bailin & Love 86; O'Raifeartaigh 86; Carmeli et al 89; Mills AJP(89)jun; Huang 92; Cheng & Li 00 [problems]; Frampton 00; Pokorski 00; 't Hooft ed-05; Quigg 13.
@ 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].
@ Geometrical approaches: Cianci et al JPA(03), add JPA(04); Catren SHPMP(08); Weatherall a1411 [and general relativity].
@ Reformulations: Faddeev & Niemi PRL(99)ht/98 [partially dual variables]; Majumdar & Sharatchandra PLB(00)ht [as ADM-type theory of metrics]; 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]; Ferreira & Luchini PRD(12)-a1205 [integral formulation]; Mitra & Sharatchandra AHEP-a1307 [dreibein and metric as prepotential]; Koenigstein et al IJMPE(16)-a1601 [from canonical transformations]; > s.a. gauge theory [variables]; Operad; sheaf theory.

Other Topics > s.a. connections; solutions; types of yang-mills theories [including curved and higher-dimensional spacetimes, generalizations].
@ General references: Śniatycki RPMP(88) [charges]; Wald in(88); Henneaux & Teitelboim PLB(90); Henneaux et al NPB(90); Śniatycki CMP(91); Shabanov PLB(01)ht [infrared limit]; Capri et al PRD(05)ht [non-local mass operator]; Marateck a0712 [rederivation].
@ 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 theory]; Pohjanpelto DG&A(04) [local, semi-simple, classification]; Strominger JHEP(14)-a1308 [asymptotic symmetries at future null infinity]; Tanzi & Giulini JHEP(20)-a2006 [asymptotic]; > s.a. conservation laws; solutions.

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