Types of Gauge Theories  

In General > s.a. gauge theory; lagrangian dynamics and systems; quantum gauge theory; types of field theories; yang-mills theory.
* Matter fields: Described by smooth cross sections of associated vector bundles, with fiber V; If we choose a basis for V at each point of M, the components of a cross section are a multiplet of particles.
* Interactions: They arise from the sections by parallel transport by the connections in the associated principal fiber bundle; Symmetry breaking corresponds to reduction of the fiber bundle.
* Massive: Mass-generating mechanisms for gauge fields are the addition of a Proca/Pauli-Fierz term, or in 3D a Chern-Simons term, to the action; The Stückelberg field method, or the Higgs mechanism in spontaneous symmetry breaking.
> Related topics: see boundaries in field theory.

Special Types > s.a. electromagnetism; parametrized; supersymmetric theories; topological field theories; types of yang-mills theories; unified theories.
* Groups: It is normally assumed that the only regularizable, and therefore viable ones (as quantum field theories) are the ones based on finite-dimensional compact gauge groups; This may not necessarily be the case.
@ Groups: Weyl SPAW(18) [gauge principle]; Pawłowski TJP(99)hp/98 [gauge theory of scale]; Brandt PRD(01)ht [spacetime symmetries]; Doplicher & Piacitelli RVMP(02)ht [any compact G is ok]; Makeenko proc(05)ht/04 [large-N, review].
@ Matter: Horan et al Pra(98)ht [charged particles]; Tolksdorf & Thumstaedter JMP(06)mp/05, Myers & Ogilvie JHEP(09)-a0903 [fermions]; García Canal & Schaposnik FJMP-a1110 [approach to coupling]; Goldman et al RPP(14)-a1308 [light-induced effective gauge fields for ultracold atoms]; > s.a. poincaré group [continuous-spin particles].
@ And spacetime transformations: Michor in(88) [diffeomorphisms]; Brodbeck HPA(96)gq; Pons et al JMP(00)gq/99 [diffeomorphisms in Einstein-Yang-Mills]; Aldaya et al JMP(03)mp/02; Minguzzi CQG(03)gq/02 [simultaneity in fiber bundle language]; Aldaya & Sánchez-Sastre gq/05-conf, JPA(06); Tresguerres IJGMP(08)-a0707 [translational symmetry]; Percacci JPA(08)-a0803 [mixing]; Wiesendanger PRD(09)-a0903 [volume-preserving diffeomorphisms]; > s.a. bianchi models; gauge theory solutions; lorentz group phenomenology; particle physics.
@ 3D: Ghosh JPA(00)ht/99 [massive Thirring], AP(01)ht/00 [master theory]; > s.a. Jackiw-Pi Theory.
@ Massive: Scharf NCA(99)ht; Deser et al AP(00), Harikumar et al PRD(01) [topologically]; Harikumar & Sivakumar MPLA(00); Deser & Tekin CQG(02)ht/02 [3D, Proca/Pauli–Fierz and Chern–Simons terms]; Acosta & Kirchbach FPL(05)gq/04 [in DSR]; Bertrand a0705-proc [topologically]; Duetsch et al a1001 [without classical Higgs mechanism]; Kruglov IJTP(11)-a1010 [Maxwell-Chern-Simons, topologically massive]; Kiriushcheva et al CJP(12)-a1112 [first-order form]; Bergshoeff et al JHEP(12)-a1207 [spin-2, topologically massive, beyond 3D]; Slavnov TMP(13) [gauge-invariant infrared regularization of Yang-Mills theory]; Vyas & Srinivasan IJTP(16)-a1510 [and quantisation]; > s.a. Proca Theory.
@ Diffeomorphism-invariant: Husain & Kuchař PRD(90); Peldán PRD(92)ht [Ashtekar-like, arbitrary G], NPB(94)gq [general-relativity-like]; Barbero et al PRD(98)gq; Husain CQG(99)ht [diff-invariant SU(N)]; > s.a. BF theory.
@ Consistent interactions: Witten PLB(82); Henneaux CM(98)ht/97 [cohomology, BRST]; Bizdadea APPB(01)ht/00, & Saliu PS(00) [BRST]; Brandt PRD(01)ht; Henneaux & Rahman PRD(13)-a1306 [gauge symmetry and causal propagation requirements].
@ Other: Vachaspati PRD(09)-a0809 [bi-fundamental fields, and cosmology]; Aharony et al JHEP(13) [different theories from the freedom in the choice of magnetic and dyonic line operators]; Bourget et al a1804 [disconnected gauge groups, principal extensions]; > s.a. Chiral Theories; gauge transformations [Lie groupoids as generalized symmetries]; Percolation; Quiver Gauge Theory.

Generalizations > s.a. lattice gauge theory; non-commutative gauge theories; non-local theories; quantum groups; yang-mills theories.
@ Non-linear: Anco JMP(97)mp/02 [3D]; Anco AP(98) [4D, spin-2 and 3/2]; Elze IJTP(08)-a0704 [and non-linear quantum mechanics]; Signori & Stiénon JGP(09) [structure group replaced by a Lie groupoid].
@ Higher-rank connections: Henneaux & Knaepen PRD(97)ht, NPB(99)ht/98, IJMPA(00)ht/99 [p-forms, consistent interactions]; Barbero & Villaseñor NPB(01)ht/00 [s-form quadratic actions]; Pfeiffer AP(03)ht, Girelli & Pfeiffer JMP(04)ht/03 [2-forms, differential vs integral]; Botta Cantcheff PLB(04) [Kalb-Ramond]; Singleton et al PLA(04) [from gauging a phase symmetry]; Baez & Schreiber ht/04 [2-connections on 2-bundles]; Akhmedov TMP(05)ht [area-ordering – {non-abelian fluxes?}]; Baez & Huerta GRG(11)-a1003-ln [introduction]; Wang JMP(14)-a1311 [3-gauge theories]; Grützmann & Strobl IJGMP(14)-a1407 [p-form gauge fields]; > s.a. Gerbes; holonomy; lattice gauge theory; quantum gauge theory.
@ Spin-2: Scharf & Wellmann ht/99; Anco PRD(03) [parity-violating deformation]; > s.a. 3D gravity.
@ Spin-3: Bekaert et al JHEP(06)ht/05 [consistent interactions]; Boulanger et al PRD(06) [parity-violating vertices]; Asorey et al PRD(15)-a1511 [symplectic gauge fields, and dark matter].
@ Higher-spin: Sezgin & Sundell JHEP(02)ht [even s]; Francia & Sagnotti CQG(03) [geometry]; Bengtsson JMP(05)ht/04, JMP(07)ht/06; Iazeolla laurea(04)ht, PhD-a0807; Bekaert & Boulanger NPB(05) [gauge invariants, Killing tensors]; Sezgin & Sundell ht/05-proc [cosmology]; Cnockaert PhD(06)ht; Guttenberg & Savvidy Sigma(08)-a0804 [Schwinger-Frønsdal theory]; Boulanger et al JHEP(08) [uniqueness of minimal coupling]; Henneaux IJGMP(08) [and N-complexes]; Bengtsson FdP(09)-a0902 [mechanical models]; Bekaert et al JHEP(09) [interactions with matter]; Manvelyan et al NPB(10), NPB(11) [cubic interactions]; Doroud & Smolin a1102 [action and Hamiltonian formulation]; Akshay & Ananth JPA(14)-a1304 [cubic interaction vertices]; Fredenhagen & Kessel JPA(15)-a1408 [frame-like and metric-like formulations]; Rivelles PRD(15)-a1408 [and continuous spin]; Sarkar & Xiao PRD(15)-a1411 [holographic representation]; Vasiliev LNP(14)-a1404 [and spacetime interpretation]; Savvidy proc(16)-a1511; Brink et al ed-16 [proc]; Casarin a1710-MS; > s.a. higher-order gravity theories; higher-spin fields; quantization; solutions.
@ Non-associative spaces: de Medeiros & Ramgoolam JHEP(05); Majid JMP(05)m.QA; Ootsuka et al ht/05 [octonionic, based on a Moufang loop]; Loginov JMP(07) [based on a Moufang loop]; > s.a. non-commutative gauge theories; Non-Associative Geometry [standard model].
@ Twisted symmetries: Aschieri et al LMP(06)ht; Vassilevich MPLA(06); Giller et al PLB(07) [consistency].
@ Discrete: Dimakis & Müller-Hoissen JPA(94); Matsuura et al PTEP(15)-a1411 [exact results]; Notarnicola et al JPA(15)-a1503 [abelian]; > s.a. lattice gauge theory; types of yang-mills theories [on a simplicial complex].
@ Other generalized spaces: Selesnick JMP(95) [quantum net]; El Baz MPLA(06) [4D quantum space]; > s.a. causal sets.
@ Other: Alfaro ht/97 [antisymmetric fields]; Jackiw ht/97; Roepstorff JMP(99)ht/98, ht/98 [superconnections on superbundles]; Brandt et al CQG(00)ht/99; Nottale et al ht/03 [in scale relativity]; Anco IJGMP(04)mp [deformations]; Lyakhovich & Sharapov NPB(04) [Poisson supermanifolds + homological vector fields]; Cuzinatto et al AP(07)ht/05 [second-order]; Aldaya et al RPMP(07) [extended gauge and diffeomorphism symmetries]; Guendelman & Steiner IJMPA(15)-a1506 [with varying effective electric charge]; Ritter et al JHEP(16)-a1512 [higher-gauge theory]; > s.a. differential forms [generalized]; generalized uncertainty principle; Notoph; Scale Relativity; types of field theory [daor].

Applications to Other Fields
@ In finance: Ilinski ht/97-proc.

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