Non-Commutative
Field Theory| Non-Commutative
Field Theory |
In General > s.a. non-commutative
geometry; energy-momentum; lattice
field theory; types of quantum field theories.
* Idea: In principle,
quantize the manifold underlying a field theory (spacetime or space) by
replacing it with a non-commutative matrix model or
a "fuzzy manifold"; In practice, replace products of fields
in the action / Hamiltonian by star products, then integrate as usual.
* Motivation:
Non-commutative spaces naturally arise in string theory with a constant background
magnetic field in the presence of D-branes; Regularize theories
while preserving their symmetries and topological features, and altogether
overcoming the fermion-doubling problem.
* Particle physics: A nice result
is that, once fermions are fixed, there is no arbitrariness in the Higgs sector.
* Result: Free 
-Minkowski
space field theory is equivalent to a relativistically invariant, non local,
free field theory on Minkowski spacetime.
> Related topics:
see
anomalies; boundaries
in field theory; CPT; fock
space; renormalization; twistors.
Types of Theories > s.a. gauge
theories [including standard model]; gravity; GUTs; non-commutative
physics; supersymmetry and susy
theories.
* Different frameworks:
Can use different star products, for example the Moyal and Wick-Voros (or normally
ordered) ones.
@ Scalar fields: Gubser & Sondhi NPB(01)
[phase structure]; Moffat PLB(01)ht/00;
Habara PTP(02)ht/01;
Bietenholz et al ht/03-in,
APPB(03)ht-in
[
4,
numerical]; Bertolami & Guisado PRD(03)
[coupled to gravity]; Daszkiewicz et al IJMPA(05)
[and DRS]; Steinacker JHEP(05)
[non-perturbative], ht/05-in
[eigenvalue distribution]; Grosse & Steinacker JHEP(06)ht [4D
self-dual 3];
Panero JHEP(07)
[numerical]; Freidel et al a0706 [free
scalar in -Minkowski];
Galluccio et al a0807,
a0807 [with Wick-Voros product].
@ Fermion fields: Gracia-Bondía et al PLB(98)ht/97,
Balachandran et al MPLA(00)
[fermion doubling]; Bourouaine & Benslama MPLA(05)ht
[Dirac, and gravity], JPA(05)
[in electromagnetic field].
@ String theory: Seiberg & Witten JHEP(99)ht;
Witten
CQG(00); Tezuka ht/01-MsSc;
Barbosa JHEP(03)ht [interpretation];
Wang ht/05 [free,
bosonic]; > s.a. String Field Theory.
@ Non-commutative target space: Balachandran et al a0706 [scalar field].
@ Other: Jack & Jones PLB(01)
[uv finite]; > s.a. 3D
quantum gravity; Born-Infeld, Gross-Neveu, Wess-Zumino
Theory.
> Related topics: see dirac
procedure; spin-statistics.
References > s.a. path integrals.
@ Intros, reviews: Kerner mp/00-in;
Douglas & Nekrasov
RMP(01)ht;
Szabo PRP(03)ht/01-ln;
Ydri ht/01-PhD;
Gracia-Bondía AdP(02)ht;
Dito & Sternheimer in(02)m.QA [history];
Girotti ht/03-ln;
Schaposnik ht/04-ln
[including solitons and instantons]; Wulkenhaar JGP(06);
Bal & Qureshi ht/06-in,
Akofor et al IJMPA(08)-a0803-in
[fuzzy physics and quantum field theory on Groenwald-Moyal plane]; Doplicher ht/06-ln.
@ Unitarity: Gomis & Mehen NPB(00)ht; Bahns et al PLB(02)ht.
@ Hamiltonian, symplectic: Neves et al JPA(04)ht/03, PRD(04)ht/03;
Vassilevich
ht/04; Abreu
et al IJMPA(06)ht/04;
> s.a. non-commutative physics.
@ And causality: Greenberg PRD(06)ht/05,
Soloviev PRD(08)-a0802 [failure
of microcausality]; Haque & Joglekar JPA(08)ht/07.
@ Properties of quantum field theories: Álvarez-Gaumé & Vázquez-Mozo
NPB(03)ht;
Bahns FdP(04)ht-in
[UV]; Smailagic & Spallucci JPA(04)
[Lorentz, unitarity, UV]; Kobayashi & Sasaki IJMPA(05)
[susy interpretation]; Panero ht/06-in
[rev]; Chaichian et al ht/06 [theorems,
rev]; [failure
of microcausality]; Gangopadhyay a0806-PhD.
@ Other formal aspects: Savvidy in(03)ht/02 [new
type]; Bozkaya et al EPJC(03)ht/02 [amplitudes
and path integrals]; Namsrai IJTP(03);
Chaichian et al ht/04 [Wightman
functions];
Paschke & Verch CQG(04)gq [covariant
quantum field theory over spectral geometries]; Mandanici & Marcianò JHEP(04)
[Heisenberg evolution]; Bahns et al PRD(05)
[Wick products]; Gonera et al PLB(05)ht [deformed
Poincaré symmetry]; Govindarajan et al MPLA(06)
[regularization]; Freidel et al PLB(07)ht [equivalence
to non-local field theory on Minkowski].
@ Phenomenology: Mariz et al PRD(07) [dispersion relations].
@ Spacetime symmetries: Iorio & Sykora IJMPA(02)ht/01 [gauge
theories]; Szabo CQG(06)ht
[and strings], ht/07-ln
[and renormalization].
@ Special backgrounds: Nakayama & Shimono PTP(04)ht [S4];
Nazaryan & Carlson PRD(05)
[non-commutative superspace].
@ Quantization: Amorim & Barcelos-Neto JPA(01)ht,
Acatrinei PRD(03)ht/02 [scalar];
Carmona et al JHEP(03);
Abe IJMPA(07)ht/06 [nc
quantization]; Chaichian et al a0706 [space
of test functions]; Daszkiewicz et al PRD(08)-a0708.
@ Perturbative effects: Minwalla et al JHEP(00)ht/99; Kossow ht/06.
@ At finite temperature:
Strelchenko & Vassilevich PRD(07)-a0705;
Fosco
& Silva JHEP-a0710 [2+1
scalar].
@ Braided quantum field theory: Oeckl CMP(01)ht/99;
Sasai
& Sasakura a0704 [Hopf
algebra symmetries and Ward-Takahashi identities].
@ Related topics: Grosse et al IJTP(96);
Kempf JMP(97)
[non-zero minimal uncertainties]; Cho et al IJMPD(00)ht/99 [propagator];
Ydri PRD(01)
[as a regulator]; Chaichian et al NPB(01)ht [non-trivial
topology]; Amelino-Camelia et al ht/02-in;
Kowalski-Glikman & Nowak PLB(02)ht,
IJMPD(03)ht/02 [and
DSR]; Barcelos-Neto ht/02 [in
curved spacetime]; Pinzul & Stern NPB(05)ht [procedure
for corrections]; Soloviev TMP(06)
[axiomatic]; Bu et al PRD(06)
[from twisted Fock space]; Aschieri et al a0708 [from
Drinfeld twist].
@ Particle physics: Chamseddine & Fröhlich PRD(94)ht/93 [SO(10)],
PLB(93)ht [Higgs
and top masses], ht/93-in
[rev];
Connes
CMP(96)ht;
Schücker ht/97-in;
Stephan ht/06 [massive
neutrinos].
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18 jul 2008