Non-Commutative
Field Theory| Non-Commutative
Field Theory |
In General > s.a. non-commutative
geometry; energy-momentum tensor; 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 (spacetimes) naturally arise in some approaches to quantum gravity; Field theories
on non-commutative spacetimes come with natural regularization parameters, 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; An issue is that models generally suffer from a manifestly
non-Wilsonian coupling of infrared and ultraviolet degrees of freedom known
as the "IR/UV problem".
* Result: Free κ-Minkowski
space field theory is equivalent to a relativistically invariant, non local,
free field theory on Minkowski spacetime.
> Related topics:
see algebraic quantum field theory; anomalies; boundaries
in field theory; CPT symmetry; fock
space; twistors.
Types of Theories > s.a. gauge
theories [including standard model]; GUTs; non-commutative
physics; supersymmetry and supersymmetric
theories.
* Different frameworks:
One 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 NPPS(04)ht/03,
APPB(03)ht-in
[λφ4,
numerical]; Bertolami & Guisado PRD(03)
[coupled to gravity]; Daszkiewicz et al IJMPA(05)
[and DRS]; Steinacker JHEP(05)
[non-perturbative], ht/05-conf
[eigenvalue distribution]; Grosse & Steinacker JHEP(06)ht [4D
self-dual φ3];
Panero JHEP(07)
[numerical]; Freidel et al IJMPA(08)-a0706 [free
scalar in κ-Minkowski];
Galluccio et al a0807,
a0807, PRD(08)-a0810 [with Wick-Voros
product]; Bertolami & Zarro PLB(09)-a0812 [coupled
to gravity, stability conditions]; Balachandran et al JHEP(11).
@ Scalar fields, Snyder spacetime: Battisti & Meljanac PRD(10)-a1003;
Girelli
& Livine JHEP(11)-a1004.
@ 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]; Bertolami & Queiroz PLA-a1105 [phase-space non-commutativity]; Verch APP-a1106-in [Dirac field on Moyal-Minkowski spacetime].
@ In curved non-commutative spacetime: Schenkel & Uhlemann Sigma(03)-a1003; Jafari a1011; Schenkel PoS-a1101.
@ String theory: Seiberg & Witten JHEP(99)ht;
Witten
CQG(00);
Tezuka MSc-ht/01;
Barbosa JHEP(03)ht [interpretation];
Wang ht/05 [free,
bosonic]; > s.a. String Field
Theory.
@ Non-commutative target space: Balachandran et al PRD(08)-a0706 [scalar
field], Sigma(10)-a1003.
@ Other: Jack & Jones PLB(01)
[ultraviolet-finite]; > s.a. 3D
quantum gravity; Born-Infeld Theory; gravity; Gross-Neveu; Wess-Zumino
Theory.
> Related topics: see dirac
procedure; Haag's Theorem; minkowski space [deformed];
particle statistics; spin-statistics
theorem.
References > s.a. path integrals;
Schwinger-Dyson Equation; non-commutative physics [Hamiltonian, time].
@ Intros, reviews: Kerner LNP(00)mp;
Douglas & Nekrasov
RMP(01)ht;
Szabo PRP(03)ht/01-ln;
Ydri PhD(01)ht;
Gracia-Bondía AdP(02)ht;
Dito & Sternheimer in(02)m.QA [history];
Girotti AJP(04)ht/03-ln;
Schaposnik ht/04-ln
[including solitons and instantons]; Wulkenhaar JGP(06);
Bal & Qureshi Sigma(06)ht-in,
Akofor et al IJMPA(08)-a0803-in
[fuzzy physics and quantum field theory on Groenwald-Moyal plane]; Doplicher
JPCS(06)ht-ln; Rivelles a1101-conf.
@ Unitarity: Gomis & Mehen NPB(00)ht; Bahns et al PLB(02)ht.
@ Hamiltonian, symplectic formalism: Neves et al JPA(04)ht/03, PRD(04)ht/03;
Vassilevich
ht/04; Abreu
et al IJMPA(06)ht/04.
@ And causality: Greenberg PRD(06)ht/05,
Soloviev PRD(08)-a0802 [failure
of microcausality]; Haque & Joglekar JPA(08)ht/07;
Balachandran et al a0905-conf
[on the Groenewold-Moyal plane]; Soloviev TMP(10)-a1012 [locality and causality].
@ Renormalizable: Bieliavsky et al JNCG(09)
[possibly finite]; Grosse & Wulkenhaar GRG(11); > s.a. renormalization.
@ 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)
[supersymmetric interpretation]; Panero Sigma(06)ht-in
[rev]; Chaichian et al ht/06 [theorems,
rev]; Gangopadhyay PhD(08)-a0806;
Saxell PLB(08)
[Lorentz-invariant, non-causality]; Bahns a1012 [IR/UV mixing problem]; van Suijlekom PLB-a1204 [almost-commutative geometries, renormalizability].
@ 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 JMP-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 space]; Kersting & Yan MPLA(08)-a0901
[IR/UV problem and coupling to gravity]; Balachandran et al PRD(10)-a0910 [inequivalence
of approaches]; Cortese & García IJMPA(10)-a1005 [Poincaré symmetry]; Akofor PhD-a1012 [symmetries, on the Moyal plane]; Basu et al JPA(11)-a1101 [relationship between the Moyal and Voros products]; Lukierski & Woronowicz a1105 [braided tensor product and covariance].
@ Phenomenology: Mariz et al PRD(07)
[dispersion relations]; Sakellariadou a0910-proc,
Nelson & Sakellariadou PRD(10) [cosmological consequences].
@ Spacetime symmetries: Iorio & Sykora IJMPA(02)ht/01 [gauge
theories]; Szabo CQG(06)ht
[and strings], AIP(07)ht [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 [non-commutative
quantization]; Chaichian et al JHEP(08)-a0706 [space
of test functions]; Daszkiewicz et al PRD(08)-a0708;
Fiore JPA(10)-a0811 [with
twisted symmetries].
@ Perturbative effects: Minwalla et al JHEP(00)ht/99;
Kossow PRD(08)ht/06.
@ At finite temperature:
Strelchenko & Vassilevich PRD(07)-a0705;
Fosco
& Silva JHEP(08)-a0710 [2+1
scalar].
@ Braided quantum field theory: Oeckl CMP(01)ht/99;
Sasai
& Sasakura PTP(07)-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-conf;
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 PRD(08)-a0708 [from
Drinfeld twist].
@ Particle physics: Chamseddine & Fröhlich PRD(94)ht/93 [SO(10)],
PLB(93)ht [Higgs
and top masses], ht/93-conf
[rev];
Connes
CMP(96)ht;
Schücker ht/97-ln;
Stephan JMP(07)ht/06 [massive
neutrinos]; van den Dungen & van Suijlekom a1204 [in almost commutative spacetime, for physicists].
main page – abbreviations – journals – comments – other
sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 19
apr 2012