Types of Field Theories  

In General > s.a. [field theory]; particle models; symmetries; 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 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.
> Related concepts: see BIon; boundaries in ft; soliton [for non-linear theories]; waves [for linear theories].

Types > s.a. Conformal, non-commutative, field theory; fluid; sigma-model [non-linear]; strings; topological field theories.
* Non-local: For example, the fractional Klein-Gordon field or modified gravity inspired by quantum loop corrections.
* Ultralocal: A field theory is ultralocal if each space point is dynamically decoupled; For example, the strong coupling limit of general relativity.
@ 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]; > s.a. higher-spin theories; statistical mechanics; types of quantum field theories.
@ Connections: Husain CQG(99)ht [diffeo-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]; Kaganovich et al ht/04-in [volume element as dynamical field]; > s.a. forms.
@ Bi-local: Naka et al PTP(05)ht/04 [q-deformed].
@ Non-local: Bergman et al PRD(02)ht/01 [and gravity duals]; Gomis et al NPB(04) [physical degrees of freedom]; Soloviev TMP(06) [and non-commutative, axiomatic]; Chicone & Mashhoon AdP(07)-a0708 [from accelerated frames]; Calcagni et al PLB(08)-a0712 [localization]; Capri et al AP(08) [gauge theories, and renormalizability]; > s.a. gravity, stochastic quantum mechanics.
@ Discrete: de Souza ht/01; Vankerschaver JMP(07)mp/06 [Euler-Poincaré reduction].
@ 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 qp/05 [charged real fields and quantum mechanics]; Jadczyk a0711 ["kairons", wavicles with initial data on timelike worldlines]; Kleinert 08 [multivalued]; Konopka MPLA(08) [with Lorentz-invariant energy scale].
> According to spin value: see scalar (including klein-gordon); low spin; high and arbitrary spin; spinors.
> Other: see approaches to quantum gravity [group field theory]; Effective Field Theory; lattice field theory; Sine-Gordon.

Integrable Field Theories > s.a. [integrable system]; Ernst Equation; QCD; self-dual; Sine-Gordon; 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].
@ KP: Dickey LMP(99) [modified]; Tu LMP(99) [q-deformed]; Kisisel mp/01, mp/01 [discretized, Hamiltonian]; Akhmetshin et al ht/02 [solutions].

Thermal Field Theory > s.a. de sitter; quantum field theory; quantum statistical mechanics [thermofield dynamics].
@ Introductions and reviews: Altherr IJMPA(93); Le Bellac 96; Landshoff hp/97-ln; Andersen & Strickland AP(05) [perturbative].
@ Finite temperature: Quirós HPA(94) [phase transitions]; Boyanovsky et al PRD(04)hp/03 [2D 4 thermalization]; Kapusta & Gale 06.

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