In General > s.a. [quantum field theory]; boundaries
in field theory;
conformal invariance; 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 [construction
of probabilistic
theories]; > s.a. types
of field theories.
@ Exactly solvable: Ushveridze MPLA(98)
[quasi-exactly solvable]; Brodsky et al AP(02) [and Pauli-Villars fields].
@ Massless: Lev TMP(04)ht/02 [massless
particles]; Aste
LMP(07)ht [self-coupling
and mass resummation].
@ Scalar: Frasca IJMPA(07)ht/06
[triviality of ![]()
4];
Loran PLB(07)ht/06 [finite-temperature
![]()
4 on
a circle]; > s.a. klein-gordon
quantum fields.
@ 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]; > s.a. ising
model.
@ Coupled
to atoms:
Hu & Raval qp/97;
Retamal et al PLA(06)
[entanglement]; > s.a. Dicke Model, Friedrichs
Model.
@ Diffeo-invariant, or background-independent: Fredenhagen & Haag CMP(87);
Kuchar in(88); Horowitz CMP(89)
[exactly soluble]; Husain PRD(93)gq [scalar,
and loop-based observables; 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;
Varadarajan PRD(04)gq [scalar,
path integral]; Dreyer
ht/04; Balachandran
et al ht/06 [on
Groenewold-Moyal plane]; Sahlmann CQG(07)gq/06 [scalar,
diffeo-invariant Hilbert space]; Campiglia et al PRD(06)gq [uniform
discretizations]; > s.a. approaches, quantum
gauge theories, parametrized, quantum
gravity.
@ 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 gq/06 [non-compact G].
@ Polymer variables:
Kaminski et al CQG(06)gq/05, CQG(06)gq [scalar];
> 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 mp/04 [massless];
Schroer ht/05-in
[rev], AP(06)ht/05 [as
testing ground]; Dorey et al ed-JPA(06)
[low-dim].
@ Other specific 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].
> Specific types:
see composite systems; dirac
quantum field theory; effective actions; QED; QCD; supersymmetric
field theory; topological theories.
Modifications and Generalizations > s.a. canonical
quantum gravity; fock
space; poincaré group; quantum
fields in curved spacetime.
* Motivation, limits of
validity: A natural UV cutoff in the validity
of quantum field theory is expected from quantum gravity or string theory,
and would help solve divergence problems.
* Galilei-invariant:
The quantum version of a field theory which is not relativistically invariant,
but only invariant under the Galilei transformations; In it, there is no particle
creation and annihilation.
* Higher-derivative theories:
They are often assumed to have ghosts, but in reality it is the fourth+second-order
theory with a mass parameter m that has ghosts, while the pure fourth-order
one is a singular limit and doesn't; This arises in the linearization of conformal
gravity.
* Non-local: Several,
differently motivated attempts at non-local (not generated by pointlike fields)
relativistic particle theories have been made,
the most recent one being quantum field theory on non-commutative spacetime.
@ Limits to quantum field theory: Cohen et al PRL(99)ht/98 [entropy
bounds and large
V's]; Carmona & Cortés
PRD(02)ht/00 [100
TeV cutoff, and quantum gravity]; > s.a. quantum
gravity phenomenology.
@ Quaternionic: Adler CMP(86); Brumby & Joshi FP(96)ht [consequences].
@ Non-Fock Hilbert spaces: Tsirelson ht/99 [fermions].
@ Finite-temperature: Ccapa Ttira et al PRD(08)-a0803 [dual
path-integral representations].
@ Generalized background: Kaiser AP(87)
[complex spacetime]; Eyink CMP(89),
CMP(89)
[fractal spacetime]; Birmingham & Rakowski MPLA(94)
[simplicial complex, intersection form action].
@ With fundamental length scale: Brüning & Nagamachi JMP(04)
[ito ultra-hyperfunctions]; Hossenfelder CQG(08)-a0712.
@ Discrete: Kur'yan in(91) [discrete spacetime]; Norton & Jaroszkiewicz
JPA(98)
[discrete t]; Häußling AP(02)
[and non-commutative geometry]; > s.a. on
graphs.
@ Deformed: Gadiyar ht/96;
Hurth & Skenderis NPB(99)ht/98,
LNP(00)ht/98 [with
symmetries]; García-Compeán et al IJMPA(01)ht/99 [scalar
and abelian gauge theory],
JPA(02)ht/01 [second
quantization of Schrödinger equation]; Kosinski et al ht/00-in, ht/00-in;
Iorio et al AP(01)ht [deformation
and curved spacetime]; Bezerra et al PRD(02), PRD(02)
[q-deformed, perturbative]; Dito m.QA/02-in
[covariant field theory]; Sardanashvily ht/02 [polysymplectic];
Hirshfeld & Henselder
AP(02)ht [star
products]; Matsuo & Shibusa MPLA(06)ht/05 [based
on gup]; > s.a. non-commutative field theory [including
braided].
@ Higher-derivative theories: Weldon AP(03);
Nguyen a0709 [self-interacting scalar field].
@ Non-local: Cornish IJMPA(92);
Breckenridge et al CQG(95)ht [in
quantised spacetime]; Barci et al IJMPA(96)ht/95;
Amorim & Barcelos-Neto
JMP(99) [non-local
massive s = 1]; Piacitelli JHEP(04)
[diagram rules]; Schroer AP(05)ht/04 [rev];
Wang
JMP(08); > s.a. causality,
quantum systems, types
of field theories.
@ Other types: Anco & Wald PRD(89)
[algebra-valued fields]; Haag CMP(93)
[characterizing models]; Ribaric & Sustersic ht/97 [transport-theoretic],
FizB(02)ht/01 [finite
alternative theory]; Yang ht/98-in, ht/98 [as
effective theory from finite
one]; Lev ht/02 [and
spin-statistics], ht/02 [supersymmetry], ht/04 [over
Galois field]; Dürr et al JPA(05)qp/04 [Bell-type
Markov processes/trajectories]; Balakov et al CMP(07)
[bilocal, scalar]; > s.a. analysis [fractional
derivatives], perfect fluids, non-standard
analysis, states [including non-equilibrium].
Main page – Abbreviations – Journals – Comments – Other
sites – Acknowledgements
Send feedback and suggestions to bombelli at olemiss.edu – Modified
11 jul 2008