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Geometries for possible kinematics

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Abstract

The physical and geometrical realizations of algebras for all possible Lorentzian and Euclidean kinematics with so(3) isotropy are presented in contraction approach and then re-classified. All geometries associated with these realizations are also obtained by the contraction method. Further relations among the geometries are revealed. Most geometries fall into pairs. There exists t ⇔ 1/(ν2 t) correspondence in each pair. In the viewpoint of differential geometry, there are only 9 geometries, which have right signature and geometrical spatial isotropy. They are 3 relativistic geometries, 3 absolute-time geometries, and 3 absolute-space geometries.

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Authors and Affiliations

  1. Institute of High Energy Physics, and Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences, Beijing, 100049, China

    ChaoGuang Huang

  2. Graduate University of Chinese Academy of Sciences, Beijing, 100049, China

    Yu Tian

  3. Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100190, China

    XiaoNing Wu

  4. Department of Physics, Tsinghua University, Beijing, 100084, China

    Zhan Xu

  5. Department of Physics, Beijing Normal University, Beijing, 100875, China

    Bin Zhou

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  1. ChaoGuang Huang
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  2. Yu Tian
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  3. XiaoNing Wu
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  4. Zhan Xu
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  5. Bin Zhou
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Correspondence to ChaoGuang Huang.

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Huang, C., Tian, Y., Wu, X. et al. Geometries for possible kinematics. Sci. China Phys. Mech. Astron. 55, 1978–2003 (2012). https://doi.org/10.1007/s11433-012-4788-4

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