Noncommutative Gauge Theories

Authors

  • M. Wohlgenannt University of Vienna, Faculty of Physics

DOI:

https://doi.org/10.15407/ujpe57.4.389

Keywords:

-

Abstract

We review two different noncommutative gauge models generalizing the approaches which lead to renormalizable scalar quantum field theories. One of them implements the crucial IR damping of the gauge field propagator in the so-called "soft breaking" part. We discuss one-loop renormalizability.

References

E. Schrödinger, Die Naturwiss. 31, 518 (1934).

https://doi.org/10.1007/BF01494946

W. Heisenberg, Ann. Phys. 32, 20 (1938).

https://doi.org/10.1002/andp.19384240105

S. Doplicher, K. Fredenhagen, and J.E. Roberts, Commun. Math. Phys. 172, 187 (1995), http://www.arXiv.org/ abs/hep-th/0303037.

https://doi.org/10.1007/BF02104515

L.J. Garay, Int. J. Mod. Phys. A 10, 145 (1995), http://arXiv.org/abs/gr-qc/9403008.

https://doi.org/10.1142/S0217751X95000085

A. Connes, M. R. Douglas, and A. S. Schwarz, JHEP 02, 003 (1998), http://www.arXiv.org/abs/hep-th/9711162.

https://doi.org/10.1088/1126-6708/1998/02/003

N. Seiberg and E. Witten, JHEP 09, 032 (1999); http://arXiv.org/abs/hep-th/9908142.

https://doi.org/10.1088/1126-6708/1999/09/032

V. Schomerus, JHEP 06, 030 (1999), http://www.arXiv.org/abs/hep-th/9903205.

https://doi.org/10.1088/1126-6708/1999/06/030

A. Connes, Inst. Hautes Etudes Sci. Publ. Math. 62, 257 (1986).

J. Bellissard, Ordinary quantum Hall effect and noncommutative cohomology. Lecture given at the Conference on Localization in Disordered System, Bad Schandau, DDR, Dec 1-5, 1986.

R. J. Szabo, Class. Quant. Grav. 23, R199 (2006), http://www.arXiv.org/abs/hep-th/0606233.

https://doi.org/10.1088/0264-9381/23/22/R01

H. S. Yang, Int. J. Mod. Phys. A 24, 4473 (2009), http://www.arXiv.org/abs/hep-th/0611174.

https://doi.org/10.1142/S0217751X0904587X

X. Calmet and A. Kobakhidze, Phys. Rev. D 74, 047702 (2006),

https://doi.org/10.1103/PhysRevD.74.047702

http://www.arXiv.org/abs/hep-th/0605275.

H. Steinacker, JHEP 12, 049 (2007), http://www.arXiv.org/abs/arXiv:0708.2426 [hep-th].

https://doi.org/10.1088/1126-6708/2007/12/049

M. Chaichian, A. Tureanu, and G. Zet, Phys. Lett. B 660, 573 (2008), http://www.arXiv.org/abs/0710.2075.

https://doi.org/10.1016/j.physletb.2008.01.029

A. P. Balachandran, A. Pinzul, B. A. Qureshi, and S. Vaidya, Phys. Rev. D 76, 105025 (2007), http://www.arXiv.org/abs/arXiv:0708.0069 [hep-th].

https://doi.org/10.1103/PhysRevD.76.105025

S. Minwalla, M. Van Raamsdonk, and N. Seiberg, JHEP 02, 020 (2000), http://www.arXiv.org/abs/hep-th/9912072.

https://doi.org/10.1088/1126-6708/2000/02/020

I.Y. Aref'eva, D.M. Belov, A.S. Koshelev, and O.A. Rytchkov, Nucl. Phys. Proc. Suppl. 102, 11 (2001), http://www.arXiv.org/abs/hep-th/0003176.

https://doi.org/10.1016/S0920-5632(01)01531-6

A. Matusis, L. Susskind, and N. Toumbas, JHEP 12, 002 (2000), http://www.arXiv.org/abs/hep-th/0002075.

https://doi.org/10.1088/1126-6708/2000/12/002

A. Micu and M.M. Sheikh Jabbari, JHEP 01, 025 (2001), http://www.arXiv.org/abs/hep-th/0008057.

https://doi.org/10.1088/1126-6708/2001/01/025

J.M. Grimstrup, H. Grosse, L. Popp, V. Putz, M. Schweda, M. Wickenhauser, and R. Wulkenhaar, Europhys. Lett. 67, 186 (2004), http://www.arXiv.org/ abs/hep-th/0202093.

https://doi.org/10.1209/epl/i2003-10285-9

H. Grosse and R. Wulkenhaar, JHEP 12, 019 (2003), http://www.arXiv.org/abs/hep-th/0307017.

https://doi.org/10.1088/1126-6708/2003/12/019

H. Grosse and R. Wulkenhaar, Commun. Math. Phys. 256, 305 (2005), http://www.arXiv.org/abs/hep-th/0401128.

https://doi.org/10.1007/s00220-004-1285-2

E. Langmann and R.J. Szabo, Phys. Lett. B 533, 168 (2002), http://www.arXiv.org/abs/hep-th/0202039.

https://doi.org/10.1016/S0370-2693(02)01650-7

M. Buric and M. Wohlgenannt, JHEP 03, 053 (2010), http://www.arXiv.org/abs/0902.3408.

R. Gurau, J. Magnen, V. Rivasseau, and A. Tanasa, Commun. Math. Phys. 287, 275 (2009), http://www.arXiv.org/ abs/0802.0791.

https://doi.org/10.1007/s00220-008-0658-3

D.N. Blaschke, H. Grosse, and M. Schweda, Europhys. Lett. 79, 61002 (2007), http://www.arXiv.org/abs/ 0705.4205.

https://doi.org/10.1209/0295-5075/79/61002

D.N. Blaschke, H. Grosse, E. Kronberger, M. Schweda, and M. Wohlgenannt, http://www.arXiv.org/abs/ 0912.3642.

A. de Goursac, J.-C. Wallet, and R. Wulkenhaar, Eur. Phys. J. C 51, 977 (2007), http://www.arXiv.org/ abs/hep-th/0703075.

https://doi.org/10.1140/epjc/s10052-007-0335-2

H. Grosse and M. Wohlgenannt, Eur. Phys. J. C 52, 435 (2007), http://www.arXiv.org/abs/hep-th/0703169.

https://doi.org/10.1140/epjc/s10052-007-0369-5

M. Buric, H. Grosse, and J. Madore, JHEP 07, 010 (2010), http://www.arXiv.org/abs/1003.2284.

D.N. Blaschke, F. Gieres, E. Kronberger, M. Schweda, and M. Wohlgenannt, J. Phys. A 41, 252002 (2008), http://www.arXiv.org/abs/0804.1914.

https://doi.org/10.1088/1751-8113/41/25/252002

D.N. Blaschke, A. Rofner, and R.I.P. Sedmik, SIGMA 6, 037 (2010), http://www.arXiv.org/abs/0908.1743.

L.C.Q. Vilar, O.S. Ventura, D.G. Tedesco, and V.E.R. Lemes, J. Phys. A 43, 135401 (2010).

https://doi.org/10.1088/1751-8113/43/13/135401

D. Zwanziger, Nucl. Phys. B 323, 513 (1989).

https://doi.org/10.1016/0550-3213(89)90122-3

D. Zwanziger, Nucl. Phys. B 399, 477 (1993).

https://doi.org/10.1016/0550-3213(93)90506-K

D.N. Blaschke, A. Rofner, R.I.P. Sedmik, and M. Wohlgenannt, http://www.arXiv.org/abs/0912.2634.

M. Hayakawa, Phys. Lett. B 478, 394 (2000), http://arXiv.org/abs/hep-th/9912094.

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Published

2012-04-30

How to Cite

Wohlgenannt, M. (2012). Noncommutative Gauge Theories. Ukrainian Journal of Physics, 57(4), 389. https://doi.org/10.15407/ujpe57.4.389

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Section

Fields and elementary particles

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