Maxwell's theory on noncommutative spaces and quaternions

Kruglov, S.I.

Maxwell's theory on noncommutative spaces and quaternions

S.I. Kruglov
(
- Intl. Educ. Ctr., Toronto
)

Oct, 2001

12 pages

Published in:

Annales Fond.Broglie 27 (2002) 343-358

e-Print:

hep-th/0110059 [hep-th]

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Abstract:

The Maxwell theory on non-commutative spaces has been considered. The non-linear equations of electromagnetic fields on non-commutative spaces were obtained in the compact spin-tensor (quaternion) form. It was shown that the plane electromagnetic wave is the solution of the system of non-linear wave equations of the second order for the electric and magnetic induction fields. We have found the canonical and symmetrical energy-momentum tensors and their non-zero traces. So, the trace anomaly of the energy-momentum tensor was obtained in electrodynamics on non-commutative spaces. It was noted that the dual transformations of electromagnetic fields on non-commutative spaces are broken.

Maxwell equation
space-time: noncommutative
quaternion
tensor: energy-momentum
duality: transformation

References(18)

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

Noncommutative QED and anomalous dipole moments

Ihab.F. Riad
(
- ICTP, Trieste
)
,
M.M. Sheikh-Jabbari
(
- ICTP, Trieste
)

- JHEP 08 (2000) 045
•
e-Print:
- hep-th/0008132
•
DOI:
- 10.1088/1126-6708/2000/08/045

C, P, and T invariance of noncommutative gauge theories

M.M. Sheikh-Jabbari
(
- ICTP, Trieste
)

- Phys.Rev.Lett. 84 (2000) 5265-5268
•
e-Print:
- hep-th/0001167
•
DOI:
- 10.1103/PhysRevLett.84.5265

Perturbative analysis on infrared aspects of noncommutative QED on R**4

M. Hayakawa
(
- KEK, Tsukuba
)

- Phys.Lett.B 478 (2000) 394-400
•
e-Print:
- hep-th/9912094
•
DOI:
- 10.1016/S0370-2693(00)00242-2

Perturbative analysis on infrared and ultraviolet aspects of noncommutative QED on R**4

M. Hayakawa
(
- KEK, Tsukuba
)

e-Print:
- hep-th/9912167

Perturbative analysis of the Seiberg-Witten map

- Int.J.Mod.Phys.A 17 (2002) 2219-2232
•
e-Print:
- hep-th/0102044
•
DOI:
- 10.1142/S0217751X02010649

The one loop UV divergent structure of U(1) Yang-Mills theory on noncommutative R**4

C.P. Martin
(
- Madrid U.
)
,
D. Sanchez-Ruiz
(
- Madrid U.
)

- Phys.Rev.Lett. 83 (1999) 476-479
•
e-Print:
- hep-th/9903077
•
DOI:
- 10.1103/PhysRevLett.83.476

Paramagnetic dominance, the sign of the beta function and UV / IR mixing in noncommutative U(1)

C.P. Martı́n
(
- Madrid U.
)
,
F. Ruiz Ruiz
(
- Madrid U.
)

- Nucl.Phys.B 597 (2001) 197-227
•
e-Print:
- hep-th/0007131
•
DOI:
- 10.1016/S0550-3213(00)00726-4

Noncommutative standard model: Model building

M. Chaichian
(
- Helsinki U. and
- Helsinki Inst. of Phys.
)
,
P. Presnajder
(
- Helsinki U. and
- Helsinki Inst. of Phys. and
- Comenius U.
)
,
M.M. Sheikh-Jabbari
(
- Helsinki U. and
- Helsinki Inst. of Phys. and
- ICTP, Trieste and
- IPM, Tehran
)
,
A. Tureanu
(
- Helsinki U. and
- Helsinki Inst. of Phys.
)

- Eur.Phys.J.C 29 (2003) 413-432
•
e-Print:
- hep-th/0107055
•
DOI:
- 10.1140/epjc/s2003-01204-7

Space-time noncommutative field theories and unitarity

Jaume Gomis
(
- Caltech and
- CIT-USC
)
,
Thomas Mehen
(
- Caltech and
- CIT-USC
)

- Nucl.Phys.B 591 (2000) 265-276
•
e-Print:
- hep-th/0005129
•
DOI:
- 10.1016/S0550-3213(00)00525-3

On theories with lightlike noncommutativity

Ofer Aharony
(
- Rutgers U., Piscataway
)
,
Jaume Gomis
(
- Caltech and
- CIT-USC
)
,
Thomas Mehen
(
- Caltech and
- CIT-USC
)

- JHEP 09 (2000) 023
•
e-Print:
- hep-th/0006236
•
DOI:
- 10.1088/1126-6708/2000/09/023

Quantized space-time

Hartland S. Snyder
(
- Northwestern U.
)

- Phys.Rev. 71 (1947) 38-41,
- In *Li, M. (ed.) et al.: Physics in non-commutative world* 3-6
•
DOI:
- 10.1103/PhysRev.71.38

The Electromagnetic Field in Quantized Space-Time

Harland S. Snyder
(
- Northwestern U.
)

- Phys.Rev. 72 (1947) 68-71
•
DOI:
- 10.1103/PhysRev.72.68

Hydrogen atom spectrum and the Lamb shift in noncommutative QED

M. Chaichian
(
- Helsinki U. and
- Helsinki Inst. of Phys.
)
,
M.M. Sheikh-Jabbari
(
- ICTP, Trieste
)
,
A. Tureanu
(
- Helsinki U. and
- Helsinki Inst. of Phys.
)

- Phys.Rev.Lett. 86 (2001) 2716
•
e-Print:
- hep-th/0010175
•
DOI:
- 10.1103/PhysRevLett.86.2716

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

Gauge theory on a quantum phase space

Luis Alvarez-Gaume
(
- CERN
)
,
Spenta R. Wadia
(
- CERN and
- Tata Inst.
)

- Phys.Lett.B 501 (2001) 319-325
•
e-Print:
- hep-th/0006219
•
DOI:
- 10.1016/S0370-2693(01)00125-3

Testing noncommutative QED, constructing noncommutative MHD

- Phys.Lett.B 517 (2001) 450-456
•
e-Print:
- hep-th/0106044
•
DOI:
- 10.1016/S0370-2693(01)00986-8

Pair production by a constant external field in noncommutative QED

N. Chair
(
- Al al-Bayt U.
)
,
M.M. Sheikh-Jabbari
(
- ICTP, Trieste
)

- Phys.Lett.B 504 (2001) 141-146
•
e-Print:
- hep-th/0009037
•
DOI:
- 10.1016/S0370-2693(01)00259-3