Chin. Phys. Lett.  2012, Vol. 29 Issue (4): 040303    DOI: 10.1088/0256-307X/29/4/040303
GENERAL |
New Geometry with All Killing Vectors Spanning the Poincaré Algebra
HUANG Chao-Guang1,2**,TIAN Yu3,WU Xiao-Ning4,5,XU Zhan6,ZHOU Bin7
1Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049
2Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences, Beijing 100049
3Graduate University of Chinese Academy of Sciences, Beijing 100049
4Institute of Mathematics, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100190
5Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190
6Department of Physics, Tsinghua University, Beijing 100084
7Department of Physics, Beijing Normal University, Beijing 100875
Cite this article:   
HUANG Chao-Guang, TIAN Yu, WU Xiao-Ning et al  2012 Chin. Phys. Lett. 29 040303
Download: PDF(474KB)  
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract The new four-dimensional geometry whose Killing vectors span the Poincaré algebra is presented and its structure is analyzed. The new geometry can be regarded as the Poincaré-invariant solution of the degenerate extension of the vacuum Einstein field equations with a negative cosmological constant and provides a static cosmological spacetime with a Lobachevsky space. The motion of free particles in the spacetime is discussed.
Received: 14 September 2011      Published: 04 April 2012
PACS:  03.30.+p (Special relativity)  
  04.20.Cv (Fundamental problems and general formalism)  
  02.20.Sv (Lie algebras of Lie groups)  
  02.90.+p (Other topics in mathematical methods in physics)  
TRENDMD:   
URL:  
https://cpl.iphy.ac.cn/10.1088/0256-307X/29/4/040303       OR      https://cpl.iphy.ac.cn/Y2012/V29/I4/040303
Service
E-mail this article
E-mail Alert
RSS
Articles by authors
HUANG Chao-Guang
TIAN Yu
WU Xiao-Ning
XU Zhan
ZHOU Bin
[1] Bacry H and Lévy-Leblond J M 1968 J. Math. Phys. 9 1605

[2] Guo H Y, Wu H T and Zhou B 2009 Phys. Lett. B 670 437

[3] Guo H Y, Huang C G, Wu H T and Zhou B 2010 Sci. Chin.–Phys. Mech. Astron. 53 591

[4] The transformations are the subset of the general fractional linear transformations by Umow N A 1910 Physik Zeit 11 905

Weyl H 1923 Mathemathische Analyse des Raumproblems (Berlin: Springer)

Fock V 1964 The Theory of Spacetime and Gravitation (Orxford: Pergamon Press) and references therein

Hua L K 1982 Starting with Unit Circle, a Lecture Note (New York: Springer-Verlag).

[5] Aldrovandi R and Pereira J G 1998 A Second Poincaré Group arXiv:gr-qc/9809061

[6] Aldrovandi R, Barbosa A L, Calçada M and Pereira J G 2003 Found. Phys. 33 613

[7] Huang C G, Tian Y, Wu X N, Xu Z and Zhou B 2012 Commun. Theor. Phys. 57 553 (in press)

[8] Ashtekar A 1986 Phys. Rev. Lett. 57 2244

Ashtekar A 1987 Phys. Rev. D 36 1587

[9] Jacobson T and Smolin L 1988 Nucl. Phys. B 299 295

Bentsson I 1989 Int. J. Mod. Phys. A 4 5527

Bentsson I 1991 Class. Quantum Grav. 8 1847

Varadarajan M 1991 Class. Quantum Grav. 8 L235

[10] Ashtekar A, Romano J D and Tate R S 1989 Phys. Rev. D 40 2572

Smolin L 2002 Quantum Gravity with a Positive Cosmological Constant arXiv:hep-th/0209079
Related articles from Frontiers Journals
[1] Gianfranco Spavieri, George T. Gillies, Miguel Rodriguez, and Maribel Perez. Effective Interaction Force between an Electric Charge and a Magnetic Dipole and Locality (or Nonlocality) in Quantum Effects of the Aharonov–Bohm Type[J]. Chin. Phys. Lett., 2021, 38(3): 040303
[2] QI Wei-Jun, REN Xin-An. From the Anti-Yang Model to the Anti-Snyder Model and Anti-De Sitter Special Relativity[J]. Chin. Phys. Lett., 2013, 30(4): 040303
[3] WU Hong-Tu, HUANG Chao-Guang, GUO Han-Ying. From the Complete Yang Model to Snyder's Model, de Sitter Special Relativity and Their Duality[J]. Chin. Phys. Lett., 2008, 25(8): 040303
[4] TU Liang-Cheng, YE Hong-Ling, LUO Jun. Variations of the Speed of Light with Frequency and Implied Photon Mass[J]. Chin. Phys. Lett., 2005, 22(12): 040303
[5] GUO Han-Ying, HUANG Chao-Guang, XU Zhan, ZHOU Bin. Three Kinds of Special Relativity via Inverse Wick Rotation[J]. Chin. Phys. Lett., 2005, 22(10): 040303
[6] CHANG Zhe, CHEN Shao-Xia, HUANG Chao-Guang. Absence of GZK Cutoff and Test of de Sitter Invariant Special Relativity[J]. Chin. Phys. Lett., 2005, 22(4): 040303
[7] LUO Shao-Kai. New Types of the Lie Symmetries and Conserved Quantities for a Relativistic Hamiltonian System[J]. Chin. Phys. Lett., 2003, 20(5): 040303
[8] LUO Shao-Kai. Form Invariance and Lie Symmetries of the Rotational Relativistic Birkhoff System[J]. Chin. Phys. Lett., 2002, 19(4): 040303
[9] AI Xiao-bai. On the Basis of Taiji Relativity[J]. Chin. Phys. Lett., 1996, 13(5): 040303
[10] YU Zurong, C. A. Nelson*. On the Coherent States and the Squeezed States[J]. Chin. Phys. Lett., 1995, 12(6): 040303
Viewed
Full text


Abstract