New Soliton Solutions in Noncommutative Torus

WEN Jun-Qing; ZHU Qiao; SHI Kang-Ji

Chinese Physics C> 2006, Vol. 30> Issue(2) : 89-93

New Soliton Solutions in Noncommutative Torus

School of Science, Xi'an Shiyou University, Xi'an 710065, China2 Institute of Modern Physics, Northwest University, Xi'an 710069, China

Abstract
HTML
Reference
Related

PDF

Abstract：
Besed on finite dimensional reduced matrices of operators on integral noncommutative torus, soliton solution problem can be converted into the finite matrix solution problem satisfying the algebraic equation Q(M)=0. In this paper, we mainly study the condition of reduced matrix for the operator which cannot be diagonalized. When the potential function V(\phi)=0 has an extremum point in three or more rank, there exist matrix solution that cannot be diagonalized for the finite dimensional matrix equation V′(M)=0$. We study the general form of the solution and construct new soliton solution on noncommutative integral ring. In terms of the construction method, we obtain soliton solutions on noncommutative orbifold.

References

[1]

Landi G. An Introduction to Non-commutative Space andTheir Geometry. arXiv:hep-th/97010782 Varilly J. Nucl.Phys., 1998, 64: 191-1963 Seiberg N, Witten E. String Theory and Non-commutativeGeometry. arXiv:hep-th/99081424 Karabali D, Nair V P. Nucl.Phys., 2002, B641: 533-5465 Douglas M R, Nekrasov N A. Rev.Mod.Phys., 2001, 73:977-10296 Martinec E J, Moore G. Noncommutative Solitons on Orbifolds. arXiv:hep-th/01011997 HOU Bo-Yu, HOU Bo-Yuan, YUE Rui-Hong. Fuzzy Sphere Bimodule and ABS Construction to The Exact Soliton Solution. arXiv:hep-th/01090918 HOU Bo-Yu, PENG Dan-Tao. Int. J. Mod. Phys., 2002,B16: 2079-20889 Derrick G. J. Math. Phys., 1964, 5: 125210 Gopakumar R, Minwalla S, Strominger A. Noncommutative Soliton. arXiv:hep-th/000316011 Harvey J. Komaba Lectures on Noncommutative Solitons and D-branes. arXiv:hepth/010207612 Harvey J, Kraus P, Larsen F. Exact Noncommutative Solitons. arXiv:hep-th/001006013 Hamanaka M, Terashima S. On Exact Noncommutative BPS Solitons. arXiv:hep-th/001022114 Gross D J, Nekrasov N A. Solitons in Noncommutative Gauge Theory. arXiv:hep-th/001009015 Gopakumar R, Headrick M, Spradin M. Commun. Math.Phys., 2003, 233: 355-38116 HOU Bo-Yu, SHI Kang-Jie, YANG Zhan-Ying. Lett. Math.Phys., 2002, 61: 205-22017 DENG Hui, HOU Bo-Yu, SHI Kang-Jie et al. J. Math.Phys., 2004,45: 978-99518 DENG Hui, HOU Bo-Yu, SHI Kang-Jie et al. The ManifestCovariant Soliton Solutions on Noncommutative Orbifold T2/Z6 and T2/Z3. arXiv:hep-th/040310219 Wong M W. Weyl Transformations. New York: Springer Verlag, 1998. 243-249

[1]	CAO Li-Ke , KE San-Min , YANG Tao , YUE Rui-Hong . Exact Solution of a New Class of Hubbard-Type Models with Open Boundary Conditions. Chinese Physics C, 2007, 31(1): 30-33.
[2]	LIAO Yi . Field Theory on Non-commutative Space-Time and Some Related Phenomenology. Chinese Physics C, 2007, 31(9): 860-863.
[3]	HE Xiao-Gang , LI Xue-Qian . Probing Noncommutative Space-Time Scale Using γγ→Z at ILC. Chinese Physics C, 2007, 31(9): 844-848.
[4]	WANG Jian-Hua , LI Kang , LIU Peng . Energy Splitting of Isotropic Harmonic Oscillator in Noncommutative Phase Space. Chinese Physics C, 2006, 30(5): 387-391.
[5]	WANG Jian-Hua , LI Kang . Split Angular Momentum in Noncommutative Phase Space. Chinese Physics C, 2006, 30(11): 1053-1057.
[6]	XIONG Hua-Hui , DENG Hui , SHI Guo-Fang , SHI Kang-Jie . Rotation and Its Realization on Noncommutative Space R^2N. Chinese Physics C, 2004, 28(8): 801-805.
[7]	SHI Guo-Fang , DENG Hui , XIONG Hua-Hui , SHI Kang-Jie . Quantum States and Soltion Solutions on Noncommutative Orbifold R4/G. Chinese Physics C, 2004, 28(10): 1033-1039.
[8]	YAN Jun , TAO Bi-You . A Electric Sine-Gordon Soliton Solution in Two-Dimensional Dilaton Gravity Model. Chinese Physics C, 2003, 27(9): 767-769.
[9]	Chen Changyuan , Liu Youwen . Exact Solutions of Non-spherical Harmonic Oscillator Potential. Chinese Physics C, 1999, 23(9): 865-872.
[10]	Ma Tao , Ni Zhixiang . Non-Harmonic Oscillator and New Conditionally Exactly Solvable Potentials. Chinese Physics C, 1999, 23(7): 650-654.
[11]	Deng Shenghua , Wang Enke , Li Jiarong . Two-Loop Effective Potential of Non-topological Soliton Bag Model at Finite Temperature. Chinese Physics C, 1995, 19(8): 713-726.
[12]	YAN Jun , TAO Bi-You , HU Shi-Ke . The Non-Abelian Wormholes Solutions in Baby Universe Model. Chinese Physics C, 1993, 17(7): 605-613.
[13]	GAO Song , WANG En-Ke , LI Jia-Rong . Bag Constant and Deconfinement Phase Transition in the Nontopological Soliton Bag Model. Chinese Physics C, 1992, 16(8): 723-730.
[14]	SIONG He-Jin , LI Jia-Rong . Soliton Star in FL-non-topological Soliton Model and Its Behavior at High Temperature. Chinese Physics C, 1992, 16(7): 600-608.
[15]	SHEN Kun , QIU Zhong-Ping . Electron-Positron Condensate and Non-Topological Soliton Model in the Strong-Coupling Phase of QED. Chinese Physics C, 1991, 15(5): 399-404.
[16]	NI Zhi-Xiang , LI Xin-Zhou . A Class of Non-Topological Solitons With Self-Interactions Φ⁴. Chinese Physics C, 1991, 15(1): 92-96.
[17]	WANG En-Ke , LI Jia-Rong . DECONFINEMENT TRANSITION OF NONTOPOLOGICAL SOLITON MODEL AT FINITE TEMPERATURE. Chinese Physics C, 1989, 13(11): 1003-1006.
[18]	XU Kai-Wen , SHEN Jian-Min . THE VIRASORO ALGEBRA ON TORUS WITH GENERAL METRIC. Chinese Physics C, 1989, 13(7): 594-599.
[19]	HUANG Nian-Ning . ON THE ONE-SOLITON SOLUTIONS OT SUPER-GORDON EGUATION. Chinese Physics C, 1985, 9(3): 382-384.
[20]	SHI YI-JIN , HE YIN . INVESTIGATION OF NON-LINFAR SCHRODINGER EQUATION SOLITON SOLUTION. Chinese Physics C, 1979, 3(4): 418-431.

Access

Get Citation

WEN Jun-Qing, ZHU Qiao and SHI Kang-Ji. New Soliton Solutions in Noncommutative Torus[J]. Chinese Physics C, 2006, 30(2): 89-93.

WEN Jun-Qing, ZHU Qiao and SHI Kang-Ji. New Soliton Solutions in Noncommutative Torus[J]. Chinese Physics C, 2006, 30(2): 89-93. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2005-04-30
Revised: 2005-10-27

Article Metric

Article Views(1321)
PDF Downloads(580)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

New Soliton Solutions in Noncommutative Torus

Corresponding author: WEN Jun-Qing,

School of Science, Xi'an Shiyou University, Xi'an 710065, China2 Institute of Modern Physics, Northwest University, Xi'an 710069, China

Received Date: 2005-04-30

Accepted Date: 2005-10-27

Available Online: 2006-02-05

Abstract: Besed on finite dimensional reduced matrices of operators on integral noncommutative torus, soliton solution problem can be converted into the finite matrix solution problem satisfying the algebraic equation Q(M)=0. In this paper, we mainly study the condition of reduced matrix for the operator which cannot be diagonalized. When the potential function V(\phi)=0 has an extremum point in three or more rank, there exist matrix solution that cannot be diagonalized for the finite dimensional matrix equation V′(M)=0$. We study the general form of the solution and construct new soliton solution on noncommutative integral ring. In terms of the construction method, we obtain soliton solutions on noncommutative orbifold.

HTML

Reference (1)

New Soliton Solutions in Noncommutative Torus

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article