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.
Types > s.a. electromagnetism; parametrized; susy
theories; topological field theories; types
of Yang-Mills theories; unified.
@ Groups: Weyl SPAW(18) [gauge principle];
Pawlowski 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 ht/04-in
[large-N,
review].
@ Matter: Horan et al Pra(98)ht [charged
particles]; Tolksdorf & Thumstaedter JMP(06)mp/05 [fermions].
@ 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-in,
JPA(06);
Tresguerres a0707 [translational
symmetry]; Percacci a0803 [mixing]; > 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]; Dayi MPLA(98)
[Hamiltonian Jackiw-Pi theory].
@ Massive: Scharf ht/99;
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-in
[topologically]; > s.a. Proca
Theory.
@ Diff-invariant: Husain & Kuchar PRD(90);
Peldán PRD(92)ht [Ashtekar-like,
arbitrary G], NPB(94)gq [gr-like];
Barbero et al PRD(98)gq;
Husain CQG(99)ht [diff-invariant
SU(N)]; Barbero & Villaseñor PRD(01)gq/00 [Husain-Kuchar
model as 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.
> Other: see BF
theory; particle
physics [quiver gauge theories]; Percolation.
Generalizations > s.a. lattice
gauge theory; non-commutative field theory; quantum
groups; Scale Relativity; 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].
@ 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,
differental 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?}]; > s.a. Gerbes, 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].
@ Higher spin in general: Sezgin & Sundell JHEP(02)ht [even
s]; Francia & Sagnotti CQG(03)
[geometry]; Bengtsson JMP(05)ht/04,
JMP(07)ht/06;
Iazeolla ht/04-laurea,
a0807-PhD; Bekaert & Boulanger NPB(05)
[gauge invariants, Killing tensors]; Sezgin & Sundell ht/05-in
[and cosmology]; Cnockaert ht/06-PhD;
Guttenberg & Savvidy a0804 [Schwinger-Frønsdal
theory]; > s.a. 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. particle
physics [standard model].
@ Twisted symmetries: Aschieri et al LMP(06)ht;
Vassilevich MPLA(06);
Giller et al PLB(07) [consistency].
@
Other generalized spaces: Dimakis & Müller-Hoissen JPA(94)
[discrete]; 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];
Behr ht/05-PhD
[con-constant commutators]; Aldaya et al RPMP(07)
[extended gauge and diffeomorphism
symmetries]; > s.a. differential
forms [generalized]; types of field theory [daor,
non-local].
Applications to Other Fields
@ In finance: Ilinski ht/97-in.
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Send feedback and suggestions to bombelli at olemiss.edu – Modified
13 jul 2008