Types of Field Theories |

**In General** > s.a. field theory;
types of quantum field theories [including algebra-valued].

* __Idea__: Models have
been studied, of fields and interactions which do not have a known realization
in nature; These may be easier to study and can give insight into the structure
of more realistic theories.

* __Massless__: Many results
obtained in field theory for massless particles do not coincide with the limit
of the corresponding results for massive particles as *m* → 0; But
the differences are due to things like mode counting, since massless particles
can only have two helicity states, which is not true for any *m* ≠ 0;
In cases where spin is not relevant (e.g., scalar particles) one does not expect
the limit to be singular.

@ __Free fields and interactions__: Lev JPA(99)qp/98;
Singh & Dadhich MPLA(01)gq [field theories from equations of motion];
> s.a. interactions.

> __Important types__: see electromagnetism;
gauge theory (and solutions); general relativity
and gravitation.

> __Types of solutions__: see BIon;
Compacton; particle models; soliton
[for non-linear theories]; waves [for linear theories].

> __Related concepts__: see boundaries in field theory;
generalized quantum field theories [finite-temperature]; symmetries.

** Specific Types** > s.a. hamiltonian systems; strings;
supersymmetric; topological field theories;
tachyons; types of quantum field theories.

* __Main types__: Local theories (the
dynamical variables are local fields, tensorial, spinorial or other), non-local theories.

* __Ultralocal__: A field
theory is ultralocal if each space point is dynamically decoupled; For example,
the strong coupling limit of general relativity.

* __Exceptional field theory__: A theory which employs
an extended spacetime to make supergravity fully covariant under the U-duality groups of M-theory.

@ __In curved spacetime__: Fabbri IJTP(11)-a0907 [causality and equivalence consistency constraints].

@ __Generally covariant__: Bergmann PR(49)
[field equations, conservation laws]; Husain CQG(92)
[2+1 model without Hamiltonian constraint]; Henneaux et al NPB(92)
[gauge invariance]; Hoppe & Ratiu CQG(97)ht/96 [Hamiltonian
reduction]; Pons CQG(03)
[diffeomorphisms and phase space], et al PRD(97)gq/96 [gauge];
in Brunetti & Fredenhagen a0901-ln; > s.a.
Covariance; diffeomorphisms; higher-spin
theories; observables; statistical
mechanics.

@ __Connections__: Husain CQG(99)ht [diffeomorphism-invariant
SU(*N*)]; > s.a. connection
form of general relativity; gauge theory.

@ __Bivectors__: Einstein & Bargmann AM(44),
Einstein AM(44);
> s.a. BF theory.

@ __Antisymmetric, forms__: Caicedo et al ht/97 [geometry];
Quevedo & Trugenberger NPB(97);
Barbero & Villaseñor PRD(02)
[4D 2-forms, kinetic terms]; Arias et al PRD(03)ht/02 [path
integral]; Guendelman et al ht/04-proc
[volume element as dynamical field]; Contreras et al PRD(10)-a1005 [duality
transformations]; Aydemir et al JPCS(10)-a1009, PRD(11) [4-form]; > s.a. brst
approach; forms.

@ __Fermions__: Robinson et al JMP(09)
[symplectic]; Skvortsov & Zinoviev NPB(11) [frame-like action]; Rejzner RVMP(11)-a1101 [functional approach]; Leclerc a1211 [symmetric Poisson bracket]; Espin a1502-proc [non-hermitian second-order Lagrangian]; Palumbo EPL(16)-a1502 [based on spinor-topological field theory, and emergent Dirac theory]; > s.a. spinors.

@ __Non-linear field equations__: Adam & Santamaria a1609 [solutions, by order reduction]; > s.a. Bogomolny Equation; sigma-model; soliton.

@ __Non-linear field space__: Mielczarek & Trześniewski PLB(16)-a1601; Mielczarek a1612 [scalar field theory, and spin].

@ __Exceptional field theory__: Hohm & Samtleben PRD(14)-a1406 [for E_{8(8)}, on (3+248)-D generalized spacetime]; Rudolph FdP(15)-a1512-proc [solutions].

@ __Discrete__: de Souza ht/01;
Vankerschaver JMP(07)mp/06 [Euler-Poincaré
reduction]; > s.a. Discretization.

@ __Fields on generalized backgrounds__: Calcagni JHEP(12)-a1107 [multi-fractional spacetime]; > s.a. cell complex; fractals in physics.

@ __Partially massless fields__: Hinterbichler & Joyce JHEP(16)-a1608, Brust & Hinterbichler JHEP(17)-a1610, JHEP(17)-a1610 [higher spin].

@ __Various dimensionalities__: Fletcher et al a1709 [features of gravity and relativistic field theory in 2D]; > s.a. higher-dimensional gravity.

@ __Other types__: Lerner & Clarke CMP(77) [massless free fields];
Guerra PRP(81) [stochastic];
Balachandran et al IJMPA(01)ht/00 [fuzzy];
Huang IJMPA(06)ht/04 [daor fields];
Akhmeteli IJQI(11)qp/05 [charged
real fields and quantum mechanics]; Jadczyk AACA(09)-a0711 ["kairons",
wavicles with initial data on timelike worldlines]; Kleinert 08 [multivalued];
Konopka MPLA(08)
[with Lorentz-invariant energy scale]; Bender & Klevansky PRL(10)-a1002 [Lagrangian describing similar
particles with different masses]; Atiyah & Moore a1009 [based on "shifted differential equations", Dirac and Einstein-Maxwell fields]; Ben Geloun JMP(12) [classical group field theories]; Jaffe et al CMP(14)-a1201 [complex, and quantum field theory].

> __According to spin value__:
see scalar fields (including klein-gordon fields); low-spin fields [including vector theories]; spin-2 fields; high
and arbitrary spin.

> __Other__: see Auxiliary Field; anomalies [relative field theories]; Conformal, Double, non-commutative, non-local field theories [including bilocal]; approaches
to quantum gravity [group field theory]; Effective
Field Theory; fluids; higher-derivative theories; lattice field theory; Sine-Gordon; Stealth Fields.

**Integrable Field Theories** > s.a. integrable
system / Ernst
Equation; QCD;
self-dual gauge fields; Sine-Gordon Equation;
wave equations[solvable].

* __KP equation__: (Kadomtsov-Petviashvili)
The equation (4 *u _{t}* – 12

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