Types
of Quantum Field Theories| Types
of Quantum Field Theories |
In General > s.a. boundaries
in field theory;
conformal invariance; generalized
and modified theories; quantum
gauge theories.
* Free vs interacting:
A field is free if the representation describing a many-particle system is
the tensor product of the corresponding single-particle representations.
@ General references: Lev qp/98;
Ratsimbarison a0706/FizB
[construction of probabilistic
theories]; > s.a. types
of field theories.
@ Exactly solvable theories: Ushveridze MPLA(98)
[quasi-exactly solvable]; Brodsky et al AP(02)
[and Pauli-Villars fields].
@ Massless fields: Lev TMP(04)ht/02 [massless
particles]; Aste
LMP(07)ht [self-coupling
and mass resummation].
@ Scalar fields: Frasca IJMPA(07)ht/06
[triviality of 
4];
Loran PLB(07)ht/06 [finite-temperature
4 on
a circle]; Brandt et al PRD(08)-a0806 [gravity-like
generalized 3,
thermal instability]; Rivasseau a0906 [zero-dimensional 4,
pedagogical]; > s.a. approaches [PT-symmetric]; klein-gordon
quantum fields; regularization;
renormalization.
@ Spin, fermion fields: Nolland & Mansfield IJMPA(00)
[fermions, Schrödinger
representation]; Iliev ht/04 [spin-1/2,
momentum picture]; Forte ht/05 [spin-statistics,
path integrals, etc]; Qiu et al IJGMP(06)ht [spin-3/2]; Kirillov &
Savelova a0810 [instability from topology fluctuations]; > s.a. ising
model.
@ Coupled
to atoms:
Hu & Raval qp/97;
Retamal et al PLA(06)
[entanglement]; Sowinski a0901 [at
finite T]; Khanna et al a0910 [thermal effects, and stability]; > s.a. Dicke
Model; Friedrichs
Model.
@ Theories of connections:
Ashtekar et al JMP(95)gq;
Bojowald & Kastrup CQG(00)ht/99 [symmetry
reduction]; Lewandowski et al CMP(06)
[uniqueness of representations];
Okolow CMP(09)gq/06 [diffeomorphism-invariant,
non-compact G].
@ Polymer variables:
Kaminski et al CQG(06)gq/05, CQG(06)gq [scalar];
Hossain et al a0906,
PRD(09)-a0906 [massless
scalar, phenomenology]; > s.a. 2D
quantum gravity; fock
space; FRW
quantum cosmology; klein-gordon fields; representations
of quantum mechanics.
@ Theories with S unbounded below:
Greensite & Halpern NPB(84) [Euclidean quantum theory]; Zavialov et al TMP(96).
@ UV-finite: Lemes et al JPA(01) [criterion].
@ Ultralocal: Klauder CMP(70),
APA(71) [quantization]; Klauder JPA(01)qp/00 [and
reparametrization-invariant quantum field theory].
@ 0+1: Boozer EJP(07) [as toy model].
@ 1+1: Derezinski & Meissner LNP(06)mp/04 [massless];
Schroer ht/05-in
[rev], AP(06)ht/05 [as
testing ground]; Dorey et al ed-JPA(06)
[low-dimensional].
@ 2+1: Robinson et al a0903 [spin-1/2
symplectic fermions].
@ Other types: Segal JMP(60),
JMP(64)
[non-linear]; Grigore JMP(95)
[free]; Chalmers JHEP(98)ht/97 [non-polynomial];
Ho et al PRE(98)qp [scalar,
open
system]; Maiani & Testa AP(98)
[unstable]; Helfer ht/99, ht/99 [bosonic];
Brouder ht/03 [degenerate
systems]; Harrivel mp/06 [scalar,
perturbative expansion]; Leclerc gq/06 [spin-2,
Faddeev-Jackiw quantization]; Carmona et al PRD-a0905 [with
modified commutation
relations].
> Specific types:
see composite systems; dirac
quantum field theory; effective actions; QED; QCD; supersymmetric
field theory.
Diffeomorphism-Invariant or Background-Independent Theories >
s.a. approaches, parametrized
theories.
@ General references: Fredenhagen & Haag CMP(87);
Kuchar in(88); Horowitz CMP(89)
[exactly soluble]; Rovelli NPB(93), JMP(95)gq [and
model for quantum geometry]; Thiemann gq/93, CQG(95)gq/99;
Salehi IJTP(97)
[dynamics formalism]; Baez & Krasnov JMP(98)
[with fermions]; Conrady et al PRD(04)
[vacuum]; Fredenhagen ht/04-in;
Dreyer ht/04;
Balachandran et al ht/06 [on
Groenewold-Moyal plane]; Campiglia et al PRD(06)gq [uniform
discretizations]; Pinamonti CMP(09)
[conformally invariant]; Neiman a0901 [degrees
of freedom over finite spatial regions].
@ Scalar fields: Husain PRD(93)gq [and
loop-based observables]; Varadarajan PRD(04)gq [path
integral]; Sahlmann CQG(07)gq/06 [diffeomorphism-invariant
Hilbert space].
> Specific types:
see quantum gauge theories; quantum
gravity; topological theories.
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send feedback and suggestions to bombelli at olemiss.edu – modified 13
nov 2009