Gauge Theories

In General > s.a. gauge transformations and gauge choices; history of physics; lorentz group phenomenology; symmetry.
* Motivation: Make a global symmetry into a local one (observers at different points can choose independently); Masslessness of gauge particles related to renormalizability (but see the Higgs mechanism); Can treat monopoles without singularities in potentials; Geometric picture of fields obtained using fiber bundle language.
* History: Principle introduced by Weyl; Fiber bundle picture appeared in the late 1960s, but was accepted only around 1973.
* Idea: The basic objects are a semisimple (in order for it to have a non-degenerate metric) Lie group G, with Lie algebra g, and a principal G-bundle P over spacetime; The variables are a g-valued connection 1-form (i e) A on this principal fiber bundle (often used interchangeably with a gauge potential, the pullback of the connection 1-form), and possibly coupled matter fields (cross-sections of associated G-bundles); If (i e) F is the curvature of the connection, and D its associated covariant derivative, one field equation is the Bianchi identity,

DF := dF + [A, F] = 0 ;

Other field equations will depend on the form of the action chosen (careful, F = dA + A A DA !).
* Applications: They are very useful (especially the non-Abelian ones) in mathematics, to get insights on 4D differential topology.
@ Texts and reviews: Göckeler & Schücker 87; Cheng & Li AJP(88)jul-RL; Chan & Tsou 93; Tsou ht/00-ln.
@ Texts, and differential geometry: Marathe & Martucci 92; Naber 97, 00.
@ A's generating the same fields: Majumdar & Sharatchandra PRD(01)ht/98.

Line / Loop and Other Variables > s.a. BF theory; connection; Field Line; holonomy; QCD; quantum gauge theory; topological field theories.
@ Wilson loops: Mandelstam AP(62); Wu & Yang PRD(75), PRD(76), PRD(76); Kozameh & Newman PRD(85) [differential holonomies and Yang-Mills equations]; Chan et al AP(86); Gambini & Trias NPB(86); Diakonov & Petrov PLB(89); Bezerra & Letelier CQG(91)refs; Rajeev & Turgut JMP(96)ht/95.
@ Gauge-invariant: Newman & Rovelli PRL(92) [lines of force]; Loll CQG(93)gq [inequalities on traces of holonomies]; Armand-Ugón et al PRD(94)ht/93 [loop variables]; Frittelli et al PRD(94) [Faraday lines]; Chechelashvili et al TMP(96)ht/95; Ganor & Sonnenschein IJMPA(96)ht/95; Haagensen ht/95, et al NPB(96)ht/95; Kijowski et al RPMP(87); Zapata JMP(97)gq [graphs]; Faddeev & Niemi PRL(99)ht/98, PLB(99)ht/98, PLB(99)ht; Blaschke et al ht/00 [topological invariants for QCD]; Orland PRD(04)ht.
@ Fluxes: Dzhunushaliev et al PLB(00) [flux tubes]; Freed et al AP(07)ht/06, CMP(07) [non-commutativity]; > s.a. lattice gauge theory [flux and charge].
@ Related topics: Brambilla & Prosperi ht/94-in [and potentials]; Watson PLB(94) [identities]; Gukov & Witten a0804 [surface opertors]; > s.a. knots in physics.

Features, Techniques > s.a. constrained systems [including reduction]; Gribov; Moduli; Seiberg-Witten; solutions.
* Configuration space: The natural one is the moduli space of all gauge equivalence classes of connections on a principal G-bundle over the spatial manifold (superspace) or connections over all such principal bundles over (grand superspace); > see connections.
* Alice configurations: Fields in theories with disconnected groups such that the disconnectedness has physical effects.
@ With boundaries: Sniatycki et al CMP(96); Avramidi & Esposito CMP(99)ht/97, gq/99-in; Ferrara & Frønsdal PLB(98)ht.
@ Measure: Pickrell JGP(96); Fleischhack mp/01, mp/01; > s.a. connection.
@ Related topics: Gomis et al PRP(95) [antibrackets]; Loll et al JGP(96) [complexification]; Lenz et al AP(00)ht [residual symmetries]; McInnes JPA(98) [Alice configurations]; Stoilov ht/05 [Lagrange multipliers]; Miskovic & Pons JPA(06)ht/05 [dynamics and symmetries of perturbations]; Feng et al JHEP(07)ht [counting gauge invariants]; Kubyshin 89 [dimensional reduction]; Anderson CQG(08)-a0711 [new interpretation of variational principle]; > s.a. manifold types [gauge orbit stratification], phase transitions; Reference Frames [accelerated].

Types of Theories and Related Concepts
> Theories: see lattice gauge theory; non-commutative field theory; types of theories and yang-mills theories.
> Related concepts: see BRST transformations; charge; energy-momentum tensor; instanton; monopole; noether symmetries; particle models.

Other References
@ General: Moriyasu 83 [primer]; Healey 07 [conceptual; r PhSc(08)oct]; Robinson et al a0810-ln [algebraic], a0908-ln [geometric].
@ Geometric picture: Lubkin AP(63); Hermann 70, 78; Trautman RPMP(70), CzJP(79); Wu & Yang PRD(75); Atiyah 79; Daniel & Viallet RMP(80); Eguchi et al PRP(80); Balachandran et al 83; Svetlichny ht/99-ln; Aldrovandi & Barbosa IJTP(00)mp/01 [non-bundle structure], IJTP(00)mp/01 [as optical medium]; Harikumar et al PLB(03)ht/02 [topology]; Kubyshin mp/03-in.
@ Meaning: de Souza ht/98, ht/99, ht/99 [discrete]; Guttmann & Lyre phy/00 [physics vs math]; Gubarev et al PRL(01)hp/00 [of A²]; Lyre qp/01-in [conceptual]; Healey PhSc(01)dec [reality of A]; 't Hooft AIP(07)-a0707 [gauge symmetry as emergent]; Sánchez a0803.

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