Nonrenormalizability of theta expanded noncommutative QED

Wulkenhaar, Raimar

doi:10.1088/1126-6708/2002/03/024

Nonrenormalizability of theta expanded noncommutative QED

Raimar Wulkenhaar
(
- Vienna U.
)

Dec, 2001

30 pages

Published in:

JHEP 03 (2002) 024

e-Print:

hep-th/0112248 [hep-th]

DOI:

10.1088/1126-6708/2002/03/024

Report number:

UWTHPH-2001-56

View in:

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Abstract:

Computing all divergent one-loop Green's functions of \theta-expanded noncommutative quantum electrodynamics up to first order in \theta, we show that this model is not renormalizable. The reason is a divergence in the electron four-point function which cannot be removed by field redefinitions. Ignoring this problem, we find however clear hints for new symmetries in massless \theta-expanded noncommutative QED: Four additional divergences which would be compatible with gauge and Lorentz symmetries and which are not reachable by field redefinitions are absent.

quantum electrodynamics: noncommutative
Seiberg-Witten map
Ward identity
n-point function
Feynman graph: higher-order

References(32)

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

Introduction to M(atrix) theory and noncommutative geometry

Anatoly Konechny
(
- UC, Berkeley and
- LBL, Berkeley
)
,
Albert S. Schwarz
(
- UC, Davis
)

- Phys.Rept. 360 (2002) 353-465
•
e-Print:
- hep-th/0012145
•
DOI:
- 10.1016/S0370-1573(01)00096-5

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

Quantum field theory on noncommutative spaces

Richard J. Szabo
(
- Heriot-Watt U.
)

- Phys.Rept. 378 (2003) 207-299
•
e-Print:
- hep-th/0109162
•
DOI:
- 10.1016/S0370-1573(03)00059-0

Noncommutative geometry and matrix theory: Compactification on tori

Alain Connes
(
- IHES, Bures-sur-Yvette
)
,
Michael R. Douglas
(
- IHES, Bures-sur-Yvette and
- Rutgers U., Piscataway
)
,
Albert S. Schwarz
(
- IHES, Bures-sur-Yvette and
- Rutgers U., Piscataway and
- UC, Davis
)

- JHEP 02 (1998) 003,
- In *Li, M. (ed.) et al.: Physics in non-commutative world* 178-206
•
e-Print:
- hep-th/9711162
•
DOI:
- 10.1088/1126-6708/1998/02/003

Divergencies in a field theory on quantum space

T. Filk
(
- Saarland U.
)

- Phys.Lett.B 376 (1996) 53-58,
- In *Li, M. (ed.) et al.: Physics in non-commutative world*
•
DOI:
- 10.1016/0370-2693(96)00024-X

Reduced Model for Large $N$ Continuum Field Theories

- Phys.Lett.B 131 (1983) 396-398
•
DOI:
- 10.1016/0370-2693(83)90526-9

Gravity coupled with matter and foundation of noncommutative geometry

Alain Connes
(
- IHES, Bures-sur-Yvette
)

- Commun.Math.Phys. 182 (1996) 155-176
•
e-Print:
- hep-th/9603053
•
DOI:
- 10.1007/BF02506388

On the ultraviolet behavior of quantum fields over noncommutative manifolds

- Int.J.Mod.Phys.A 14 (1999) 1305
•
e-Print:
- hep-th/9804001
•
DOI:
- 10.1142/S0217751X99000671

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

Renormalizability of the supersymmetric Yang-Mills theories on the noncommutative torus

M.M. Sheikh-Jabbari
(
- IPM, Tehran
)

- JHEP 06 (1999) 015
•
e-Print:
- hep-th/9903107
•
DOI:
- 10.1088/1126-6708/1999/06/015

Perturbative quantum gauge fields on the noncommutative torus

Thomas Krajewski
(
- Marseille, CPT and
- Provence U.
)
,
Raimar Wulkenhaar
(
- Marseille, CPT and
- Leipzig U.
)

- Int.J.Mod.Phys.A 15 (2000) 1011-1030
•
e-Print:
- hep-th/9903187
•
DOI:
- 10.1142/S0217751X00000495

Renormalization of noncommutative U(N) gauge theories

L. Bonora
(
- SISSA, Trieste and
- INFN, Trieste
)
,
M. Salizzoni
(
- SISSA, Trieste and
- INFN, Trieste
)

- Phys.Lett.B 504 (2001) 80-88
•
e-Print:
- hep-th/0011088
•
DOI:
- 10.1016/S0370-2693(01)00281-7

Comments on perturbative dynamics of noncommutative Yang-Mills theory

Adi Armoni
(
- Ecole Polytechnique
)

- Nucl.Phys.B 593 (2001) 229-242,
- In *Li, M. (ed.) et al.: Physics in non-commutative world* 452-463
•
e-Print:
- hep-th/0005208
•
DOI:
- 10.1016/S0550-3213(00)00557-5

Noncommutative perturbative dynamics

Shiraz Minwalla
(
- Princeton U.
)
,
Mark Van Raamsdonk
(
- Princeton U.
)
,
Nathan Seiberg
(
- Princeton, Inst. Advanced Study
)

- JHEP 02 (2000) 020,
- In *Li, M. (ed.) et al.: Physics in non-commutative world* 426-451
•
e-Print:
- hep-th/9912072
•
DOI:
- 10.1088/1126-6708/2000/02/020