Non-Commutative Field Theory| Non-Commutative Field Theory |
In General > s.a. non-commutative geometry;
energy-momentum tensor; lattice
field theory [including fermion doubling]; types of 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-conf
[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);
Bietenholz et al JPCS(15)-a1402;
Rea & Sämann JHEP(15)-a1507 [scalar field theory on the fuzzy disc, phase diagram].
@ Scalar fields, Snyder spacetime:
Battisti & Meljanac PRD(10)-a1003;
Girelli & Livine JHEP(11)-a1004;
> s.a. modified quantum field theories..
@ 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(11)-a1105 [phase-space non-commutativity];
Verch APP-a1106-proc [Dirac field on Moyal-Minkowski spacetime];
Williams & Scholtz a1512
[manifestly Lorentz covariant, interacting and non-commutative Dirac equation].
@ In curved non-commutative spacetime: Schenkel & Uhlemann Sigma(03)-a1003;
Jafari a1011;
Schenkel PoS-a1101;
Franchino-Viñas & Mignemi a2104
[Snyder-de Sitter space, φ4 theory].
@ 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];
Heckman & Verlinde NPB(15)-a1401 [covariant non-commutative deformation of 4D cft];
Zois a1401-conf
[non-commutative topological quantum field theory and non-commutative Floer homology];
> 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;
statistical mechanics.
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-proc,
Akofor et al IJMPA(08)-a0803-ln [fuzzy physics and quantum field theory on Groenwald-Moyal plane];
Doplicher JPCS(06)ht;
Rivelles JPCS(11)-a1101;
Chaichian et al NPB(20)-a2001 [axiomatic formulation].
@ 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,
PRD(06);
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-conf [UV];
Smailagic & Spallucci JPA(04) [Lorentz, unitarity, UV];
Kobayashi & Sasaki IJMPA(05) [supersymmetric interpretation];
Panero Sigma(06)ht-proc [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(12)-a1204 [almost-commutative geometries, renormalizability];
Labuschagne & Majewski a1702 [integral and differential structures].
@ 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(11)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 JPA(12)-a1105 [braided tensor product and covariance];
> s.a. quantum field theory techniques [worldline approach].
@ Phenomenology: Mariz et al PRD(07) [dispersion relations];
Kurkov et al PLB(14)-a1312 [high-energy bosons do not propagate];
Vassilevich JPCS(16)-a1510 [bosonic fields at very high energies];
> s.a. 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;
Samary et al EPJC(14)-a1406 [pair production of Dirac particles].
@ 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 RVMP(12)-a1204 [in almost commutative spacetime, for physicists];
Gargiulo et al EPJC(14)-a1305 [algebra doubling and neutrino mixing].
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 2 apr 2021