Non-commutative phase space and its space-time symmetry

LI Kang; Dulat Sayipjamal

doi:10.1088/1674-1137/34/7/003

Chinese Physics C> 2010, Vol. 34> Issue(7) : 944-948 DOI: 10.1088/1674-1137/34/7/003

Non-commutative phase space and its space-time symmetry

LI Kang ^, ,
Dulat Sayipjamal ,

Abstract
HTML
Reference
Related

PDF

Abstract：
First a description of 2+1 dimensional non-commutative (NC) phase space is presented, and then we find that in this formulation the generalized Bopp's shift has a symmetric representation and one can easily and straightforwardly define the star product on NC phase space. Then we define non-commutative Lorentz transformations both on NC space and NC phase space. We also discuss the Poincare symmetry. Finally we point out that our NC phase space formulation and the NC Lorentz transformations are applicable to any even dimensional NC space and NC phase space.

References

[1]

. Seiberg N, Witten E. JHEP, 1999, 032: 99092. Chaichian M, Sheikh-Jabbari M M, Tureanu A. Phys. Rev.Lett., 2001 86: 2716; Chaichian M, Demichev A, Presna-jder P, Sheikh-Jabbari M M, Tureanu A. Nucl. Phys. B,2001, 611: 383; 2004, 70: 14-343. Chaichian M, Presnajder P, Sheikh-Jabbari M M, TureanuA. Phys. Lett. B, 2002, 527: 149-154; Falomir H, GamboaJ, Loewe M, Mendez F, Rojas J C. Phys. Rev. D, 2002, 66:045018; Omer F D, Ahmed J. J. Math. Phys., 2002, 43:45924. LI K, Dulat S. Eur. Phys. J. C, 2006, 46: 825; LI K,WANG J. Eur. Phys. J. C, 2007, 50: 1007; J. Phys. A:Math Theor., 2007 40 : 21975. Mirza B, Zarei M. Eur. Phys. J. C, 2004, 32: 583; MirzaB, Narimani R, Zarei M. Eur. Phys. J. C,2006, 48: 6416. LI K, WANG J, CHEN C. Mod. Phys. Lett. A, 2005, 20:2165-21747. Demetrian M, Kochan D. 2001, hep-th/0102050; ZHANGJ. Phys. Lett. B, 2004, 584: 2048. Calmet X. Phys. Rev. D, 2005, 71: 0850129. Wess J. 2004, hep-th/0408080; Chaichian M, Kulish P P,Nishijima K, Tureanu A. Phys. Lett. B, 2004, 604: 9810. Lukierski J, Nowicki A, Ruegg H. Phys. Lett. B, 1992, 293:34411. Gomis J, Mehen T. Nucl. Phys. B, 2000, 591: 26512. Alvarez Gaume L, Barbon J L F, Zwicky R. JHEP, 2001,05: 05713. Seiberg N, Susskind L, Toumbas N. JHEP, 2000, 06: 04414. Alvarez-Gaume L, Wadia Spenta R. Phys. Lett. B, 2001,501: 319; CHU S C. Nucl. Phys. B, 1999, 550: 151

[1]	S. Parsamehr , M. Mohsenzadeh . Gauge theory of massless spin-(3/2) field in de Sitter space-time. Chinese Physics C, 2016, 40(11): 113102. doi: 10.1088/1674-1137/40/11/113102
[2]	S. S. Hosseini , S. Zarrinkamar . Dirac oscillator in noncommutative space. Chinese Physics C, 2014, 38(6): 063104. doi: 10.1088/1674-1137/38/6/063104
[3]	MA Meng-Sen , ZHAO Hui-Hua . Quantized space-time and its influence on two physical problems. Chinese Physics C, 2014, 38(4): 045102. doi: 10.1088/1674-1137/38/4/045102
[4]	LIANG Mai-Lin , ZHANG Ya-Bin , YANG Rui-Lin , ZHANG Fu-Lin . Dirac equation with a magnetic field in 3D non-commutative phase space. Chinese Physics C, 2013, 37(6): 063106. doi: 10.1088/1674-1137/37/6/063106
[5]	JIN Dan , YANG Ya-Dong . Space- and time-like kaon electromagnetic form factors in perturbative QCD. Chinese Physics C, 2012, 36(10): 941-946. doi: 10.1088/1674-1137/36/10/004
[6]	YAN Mu-Lin . Evidence for special relativity with de Sitter space-time symmetry. Chinese Physics C, 2011, 35(3): 228-232. doi: 10.1088/1674-1137/35/3/004
[7]	ZHOU Hai-Qing . Two-photon-exchange contribution to proton form factors in both space-like and time-like regions. Chinese Physics C, 2010, 34(6): 869-873. doi: 10.1088/1674-1137/34/6/042
[8]	YUAN Yi , LI Kang , WANG Jian-Hua , CHEN Chi-Yi . Spin-1/2 relativistic particle in a magnetic field in NC phase space. Chinese Physics C, 2010, 34(5): 543-547. doi: 10.1088/1674-1137/34/5/005
[9]	REN Yan-Yu , Efaaf M , ZHANG Wei-Ning . Inhomogeneous space-time structure and two-pion interferometry in NEXSPHERIO model. Chinese Physics C, 2010, 34(4): 472-478. doi: 10.1088/1674-1137/34/4/010
[10]	DONG Yu-Bing . Pion charge form factor and constraints from space-time translations. Chinese Physics C, 2010, 34(9): 1342-1345. doi: 10.1088/1674-1137/34/9/038
[11]	S. Pacetti¹ , 2 . Nucleon form factors: the space-time connection. Chinese Physics C, 2010, 34(6): 874-876.
[12]	WANG Jian-Hua , LI Kang , Dulat Sayipjamal , . Klein-Gordon oscillators in noncommutative phase space. Chinese Physics C, 2008, 32(10): 803-806. doi: 10.1088/1674-1137/32/10/007
[13]	WEI Gao-Feng , LONG Chao-Yun , LONG Zheng-Wen , QIN Shui-Jie . Exact solution to two-dimensional isotropic charged harmonic oscillator in uniform magnetic field in non-commutative phase space. Chinese Physics C, 2008, 32(4): 247-250. doi: 10.1088/1674-1137/32/4/001
[14]	WEI Gao-Feng , LONG Chao-Yun , LONG Zheng-Wen , QIN Shui-Jie , FU Qiang . Classical mechanics in non-commutative phase space. Chinese Physics C, 2008, 32(5): 338-341. doi: 10.1088/1674-1137/32/5/002
[15]	LIAO Yi . Field Theory on Non-commutative Space-Time and Some Related Phenomenology. Chinese Physics C, 2007, 31(9): 860-863.
[16]	Wang Shaoshun , Zhang Jie , Ye Yunxiu , Xiao Chenguo . Ratio of Factorial Cumulant to Factorial Moment Versus the Size of Phase Space. Chinese Physics C, 1996, 20(S4): 307-312.
[17]	Zhuang Pengfei , Liu Lianshou . Estimation of the Maximum Energy Density in High Energy Heavy Ion Collisions and the Space-time Region for the Formation of Quark Matter. Chinese Physics C, 1991, 15(S3): 297-305.
[18]	Mao Naifeng , Li Zenghai . Spline Function Representation For Transformation of Beam Phase Space With Arbitrary Contours. Chinese Physics C, 1989, 13(S2): 149-156.
[19]	Xu Kaiwen . Covariant and Quantization of Spinning String in M_d × G Space Time. Chinese Physics C, 1988, 12(S2): 143-152.
[20]	XU BO-WEI . SPACE-TIME PROPERTY OF FERMION NUMBER. Chinese Physics C, 1979, 3(1): 60-66.

Access

Get Citation

LI Kang, Dulat Sayipjamal and Non-commutative phase space and its space-time symmetry[J]. Chinese Physics C, 2010, 34(7): 944-948. doi: 10.1088/1674-1137/34/7/003

LI Kang, Dulat Sayipjamal and Non-commutative phase space and its space-time symmetry[J]. Chinese Physics C, 2010, 34(7): 944-948. doi: 10.1088/1674-1137/34/7/003 shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2009-07-28
Revised: 2009-11-25

Article Metric

Article Views(2577)
PDF Downloads(679)
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

Non-commutative phase space and its space-time symmetry

Corresponding author: LI Kang,

Received Date: 2009-07-28

Accepted Date: 2009-11-25

Available Online: 2010-07-05

Abstract:

First a description of 2+1 dimensional non-commutative (NC) phase space is presented, and then we find that in this formulation the generalized Bopp's shift has a symmetric representation and one can easily and straightforwardly define the star product on NC phase space. Then we define non-commutative Lorentz transformations both on NC space and NC phase space. We also discuss the Poincare symmetry. Finally we point out that our NC phase space formulation and the NC Lorentz transformations are applicable to any even dimensional NC space and NC phase space.

HTML

Reference (1)

Non-commutative phase space and its space-time symmetry

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article