Remarks on Exactly Solvable Noncommutative Quantum Field

Chin. Phys. Lett.

2007, Vol. 24

Issue (6): 1509-1512 DOI:

Original Articles

Remarks on Exactly Solvable Noncommutative Quantum Field

WANG Ning

Department of Physics, Ocean University of China, Qingdao 266003

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WANG Ning 2007 Chin. Phys. Lett. 24 1509-1512

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Abstract We study exactly the solvable noncommutative scalar quantum field models of (2n) or (2n+1) dimensions. By writing out an equivalent action of the noncommutative field, it is shown that the special condition B.θ=±I in field theoretic context means the full restoration of the maximal U (∞) gauge symmetries broken due to kinetic term. It is further shown that the model can be obtained by dimensional reduction of a 2n-dimensional exactly solvable
noncommutative Ф⁴ quantum field model closely related to the 1+1-dimensional Moyal/matrix-valued nonlinear Schrodinger (MNLS) equation. The corresponding quantum fundamental commutation relation of the MNLS model is also given explicitly.

Keywords: 11.10.Nx 02.30.Ik

Received: 06 November 2006 Published: 17 May 2007

PACS:	11.10.Nx	(Noncommutative field theory)
	02.30.Ik	(Integrable systems)

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https://cpl.iphy.ac.cn/ OR https://cpl.iphy.ac.cn/Y2007/V24/I6/01509

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[2] Gopakumar R et al 2003 Commun. Math. Phys. 233 355
[3] Aganagic M et al 2001 J. High Energy Phys. 0104 001
[4] Nekrasov N A et al 1998 Commun. Math. Phys. 198 689
[5] Gross D J and Nekrasov N A 2000 J. High Energy Phys. 0007 034
[6] Polychronakos A P 2000 Phys. Lett. B 495 407
[7] Jatkar D J et al 2000 J. High Energy Phys. 0009 018
[8] Dasgupta K et al 2000 J. High Energy Phys. 0006 022
[9] Harvey J A et al 2000 J. High Energy Phys. 0007 042
[10] Mandal G and Rey S J 2000 Phys. Lett. B 495 193
[11] Witten E Noncommutative Tachyons and String Field Theory
[arXiv: hep-th/0006071]
[12] Mandal G et al 2002 Eur. Phys. J. C 24 495
[13] Langmann E et al 2004 J. High Energy Phys. 0401 017
[14] Langmann E et al 2003 Phys. Lett. B 569 95
[15] Langmann E and Szabo R J 2002 Phys. Lett. B 533 168
[16] Ambj\'\o rn J et al 1999 J. High Energy Phys. 9911 029
[17] Kim S et al 2002 Phys. Rev. D 65 045009
[18] Seiberg N and Witten E 1999 J. High Energy Phys. 9909 032
[19] Seiberg N 2000 J. High Energy Phys. 0009 003
[20] Nair V P and Polychronakos A P 2001 Phys. Lett. B 505 267
[21] Bellucci S et al 2001 Phys. Lett. B 522 345
[22] Langmann E 2003 Nucl. Phys. B 654 404
[23] Wang N and Wadati M 2003 J. Phys. Soc. Jpn. 72 3055
[24] Sklyanin E K 1979 Sov. Phys. Dokl. 24 107 Sklyanin E K 1982 J. Sov. Math. 19 1546
[25] Kulish P P and Sklynin E K 1982 J. Sov. Math. 19 1596
[26] Faddeev L D 1981 Sov. Sci. Rev. Math. Phys. C 1 107
[27] Thacker H B 1983 Rev. Mod. Phys. 53 253
[28] Polychronakos A P 2005 Nucl. Phys. B 711 505
[29] Korepin V E et al 1993 Quantum Inverse Scattering Method andCorrelation Functions (London: Cambridge University Press)

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