Types of Gauge Theories| 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];
Dütsch et al EPJC(10)-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)];
Barbero et al JHEP(19)-a1906 [Husain-Kuchař model on manifolds with boundary];
> 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 NPB(19)-a1804 [disconnected gauge groups, principal extensions];
Kapoor a2104 [axial vector gauge theory];
> s.a. Chiral Theories; gauge transformations [Lie groupoids
as generalized symmetries]; Percolation; Quiver
Gauge Theory; stochastic quantization [axial vector 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;
Kuzenko & Ponds JHEP(18)-a1806 [topologically massive];
Vuković a1809-MS [rev];
Steinacker a1911 [and gravity];
> 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.
@ Higher gauge theories:
Ritter et al JHEP(16)-a1512 [generalization related to double field theory];
Asante et al a1908 [and quantum geometry];
Radenković & Vojinović a2005-proc [examples].
@ 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];
Canarutto a2011 [without groups];
> 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.
main page
– abbreviations
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