Reduced systems of (2,2) pseudo-euclidean noncommutative self-dual Yang-Mills theories

Legare, M.

doi:10.1088/0305-4470/35/26/310

Reduced systems of (2,2) pseudo-euclidean noncommutative self-dual Yang-Mills theories

M. Legare
(
- Alberta U.
)

2002

9 pages

Published in:

J.Phys.A 35 (2002) 5489-5497

DOI:

10.1088/0305-4470/35/26/310

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Abstract: (IOP)

Self-dual Yang–Mills equations on noncommutative spaces associated with pseudo-Euclidean space of signature (2, 2) are shown to be related via dimensional reductions to noncommutative formulations of Toda equations, of generalized nonlinear Schrödinger (NS) equations, of the super-Korteweg–de Vries (super-KdV) as well as of the matrix KdV equations. The noncommutative extensions of their linear systems and bicomplexes associated with conserved quantities are discussed as well. Aq-plane version of the KdV equation with linear system is also shown.

gauge field theory: Yang-Mills
field theory: noncommutative
duality
dimensional reduction
Korteweg-de Vries equation
field equations: Toda
Schroedinger equation: nonlinear

References(34)

Figures(0)

String theory and noncommutative geometry

- JHEP 09 (1999) 032,
- In *Li, M. (ed.) et al.: Physics in non-commutative world* 327-401
•
e-Print:
- hep-th/9908142
•
DOI:
- 10.1088/1126-6708/1999/09/032

Open N=2 strings in a B field background and noncommutative selfdual Yang-Mills

- Phys.Lett.B 507 (2001) 317-326
•
e-Print:
- hep-th/0012200
•
DOI:
- 10.1016/S0370-2693(01)00454-3

Teleparallel gravity and dimensional reductions of noncommutative gauge theory

- Phys.Rev.D 64 (2001) 104019
•
e-Print:
- hep-th/0105094
•
DOI:
- 10.1103/PhysRevD.64.104019

Gauge theory on noncommutative spaces

John Madore
(
- Orsay, LPT and
- Munich, Max Planck Inst.
)
,
Stefan Schraml
(
- Munich, Max Planck Inst. and
- Munich U.
)
,
Peter Schupp
(
- Munich U.
)
,
Julius Wess
(
- Munich, Max Planck Inst. and
- Munich U.
)

- Eur.Phys.J.C 16 (2000) 161-167
•
e-Print:
- hep-th/0001203
•
DOI:
- 10.1007/s100520050012

Noncommutative field theory

Michael R. Douglas
(
- Rutgers U., Piscataway and
- IHES, Bures-sur-Yvette
)
,
Nikita A. Nekrasov
(
- IHES, Bures-sur-Yvette and
- Moscow, ITEP
)

- Rev.Mod.Phys. 73 (2001) 977-1029
•
e-Print:
- hep-th/0106048
•
DOI:
- 10.1103/RevModPhys.73.977

Scattering of noncommutative solitons in (2+1)-dimensions

Olaf Lechtenfeld
(
- Hannover U.
)
,
Alexander D. Popov
(
- Hannover U.
)

- Phys.Lett.B 523 (2001) 178-184
•
e-Print:
- hep-th/0108118
•
DOI:
- 10.1016/S0370-2693(01)01323-5

Exact noncommutative solitons

Jeffrey A. Harvey
(
- Chicago U., EFI and
- Chicago U.
)
,
Per Kraus
(
- Chicago U., EFI and
- Chicago U.
)
,
Finn Larsen
(
- Chicago U., EFI and
- Chicago U.
)

- JHEP 12 (2000) 024
•
e-Print:
- hep-th/0010060
•
DOI:
- 10.1088/1126-6708/2000/12/024

Solitons in noncommutative gauge theory

David J. Gross
(
- Santa Barbara, KITP
)
,
Nikita A. Nekrasov
(
- Moscow, ITEP and
- Princeton U. and
- IHES, Bures-sur-Yvette
)

- JHEP 03 (2001) 044
•
e-Print:
- hep-th/0010090
•
DOI:
- 10.1088/1126-6708/2001/03/044

Bicomplexes, integrable models, and noncommutative geometry

- Int.J.Mod.Phys.B 14 (2000) 2455-2460
•
e-Print:
- hep-th/0006005
•
DOI:
- 10.1142/S0217979200001977

A Noncommutative version of the nonlinear Schrodinger equation

e-Print:
- hep-th/0007015

Noncommutative Korteweg-de Vries equation

e-Print:
- hep-th/0007074

Moyal deformation, Seiberg-Wittenmap, and integrable models

- Lett.Math.Phys. 54 (2000) 123-135
•
e-Print:
- hep-th/0007160
•
DOI:
- 10.1023/A:1011028111581

Deformation quantization of sdiff(sigma(2)) SDYM equation

M. Przanowski
(
- CINVESTAV, IPN and
- Lodz, Tech. U.
)
,
J.F. Plebanski
(
- CINVESTAV, IPN
)
,
S. Formanski
(
- Lodz, Tech. U.
)

e-Print:
- hep-th/0107211

- Math.Res.Lett. 4 413

NonAbelian integrable systems, quasideterminants, and Marchenko Lemma

Pavel Etingof
(
- Harvard U.
)
,
Israel Gelfand
(
- Rutgers U., Piscataway
)
,
Vladimir Retakh
(
- Harvard U.
)

e-Print:
- q-alg/9707017

Exact noncommutative KP and KdV multisolitons

L.D. Paniak
(
- Princeton U.
)

e-Print:
- hep-th/0105185

Instantons on noncommutative R**4 and (2,0) superconformal six-dimensional theory

Nikita Nekrasov
(
- Moscow, ITEP and
- Harvard U.
)
,
Albert S. Schwarz
(
- UC, Davis
)

- Commun.Math.Phys. 198 (1998) 689-703,
- In *Li, M. (ed.) et al.: Physics in non-commutative world* 468-483
•
e-Print:
- hep-th/9802068
•
DOI:
- 10.1007/s002200050490

Noncommutative instantons and twistor transform

- Commun.Math.Phys. 221 (2001) 385-432
•
e-Print:
- hep-th/0002193
•
DOI:
- 10.1007/PL00005576

Anti-selfdual Yang-Mills equations on noncommutative space-time

Kanehisa Takasaki
(
- Kyoto U., FIHS
)

- J.Geom.Phys. 37 (2001) 291-306
•
e-Print:
- hep-th/0005194
•
DOI:
- 10.1016/S0393-0440(00)00056-5

Enveloping algebra valued gauge transformations for nonAbelian gauge groups on noncommutative spaces

Branislav Jurco
(
- Bonn, Max Planck Inst., Math.
)
,
Stefan Schraml
(
- Munich, Max Planck Inst. and
- Munich U.
)
,
Peter Schupp
(
- Munich U.
)
,
Julius Wess
(
- Munich, Max Planck Inst. and
- Munich U.
)

- Eur.Phys.J.C 17 (2000) 521-526
•
e-Print:
- hep-th/0006246
•
DOI:
- 10.1007/s100520000487

Supermatrix KdV and supergeneralized NS equations from selfdual Yang-Mills systems with supergauge groups

J. LaChapelle
(
- Alberta U.
)
,
M. Legare
(
- Alberta U.
)

- Lett.Math.Phys. 45 (1998) 195-202
•
e-Print:
- hep-th/9804112
•
DOI:
- 10.1023/A:1007403004107

- Am.J.Math. 119 609

Bidifferential calculi and integrable models

- J.Phys.A 33 (2000) 957
•
e-Print:
- math-ph/9908015
•
DOI:
- 10.1088/0305-4470/33/5/311

Selfdual Yang-Mills fields in D = 4 and integrable systems in 1 $\le$ D $\le$ 3

T.A. Ivanova
(
- Dubna, JINR
)
,
A.D. Popov
(
- Dubna, JINR
)

- Theor.Math.Phys. 102 (1995) 280-304,
- Teor.Mat.Fiz. 102 (1995) 384-419
•
DOI:
- 10.1007/BF01017880

Quantum mechanics as a statistical theory

J.E. Moyal
(
- Queen's U., Belfast
)

- Math.Proc.Cambridge Phil.Soc. 45 (2008) 1, 99-124,
- Proc.Cambridge Phil.Soc. 45 (1949) 99-124,
- In *Li, M. (ed.) et al.: Physics in non-commutative world* 9-33
•
DOI:
- 10.1017/S0305004100000487

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