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 field theory results obtained 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 in an extended spacetime that makes supergravity fully covariant under the U-duality groups of M-theory; > s.a. Extended.
@ 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 LNP(09)-a0901; > 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; canonical formulation of gravity [covariant]; 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 JHEP(16)-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]; Berman a1903-proc [Kaluza-Klein approach].
@ 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]; Huang IJMPA(06)ht/04 [daor fields]; Akhmeteli IJQI(11)qp/05 [charged real fields and quantum mechanics]; 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]; Curtright NPB(19)-a1907 [4D massive dual fields].
@ Generalized: Balachandran et al IJMPA(01)ht/00 [fuzzy]; Jadczyk AACA(09)-a0711 ["kairons", wavicles with initial data on timelike worldlines]; Kleinert 08 [multivalued]; Gorantla et al a2007 [non-standard theories related to fractons].
> 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 ut − 12 u ux − uxxx)x = 3 uyy; A completely integrable system.
* Other examples: 2D field theories obtained from 4D ones using isometry groups (> see solutions of general relativity with symmetries and generating methods).
@ General references: Alvarez et al NPB(98) [new approach, any dimension];
Andrianov et al JPA(99)si/98 [and supersymmetric quantum mechanics]; Lorente in(00)qp/04, JCAM(03)mp/04 [on the lattice]; Papachristou a0803 [symmetry and integrability]; Ferreira et al AIP(13)-a1307 [quasi-integrable theories].
@ KP: Dickey LMP(99) [modified]; Tu LMP(99) [q-deformed]; Kisisel mp/01, mp/01 [discretized, Hamiltonian]; Akhmetshin et al ht/02 [solutions].

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