New Soliton Solutions in Noncommutative Torus

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

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《中国物理C》（英文）编辑部

2024年10月30日

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

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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

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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

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

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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.