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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