Symmetries in a very special relativity and isometric group of Finsler space

  • We present an explicit connection between the symmetries in a Very Special Relativity (VSR) and isometric group of a specific Finsler space. It is shown that the line element that is invariant under the VSR symmetric group is a Finslerian one. The Killing vectors in Finsler space are constructed in a systematic way. The Lie algebras corresponding to the symmetries of VSR are obtained from a geometric famework. The dispersion relation and the Lorentz invariance violation effect in the VSR are discussed.
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LI Xin, CHANG Zhe and MO Xiao-Huan. Symmetries in a very special relativity and isometric group of Finsler space[J]. Chinese Physics C, 2011, 35(6): 535-538. doi: 10.1088/1674-1137/35/6/004
LI Xin, CHANG Zhe and MO Xiao-Huan. Symmetries in a very special relativity and isometric group of Finsler space[J]. Chinese Physics C, 2011, 35(6): 535-538.  doi: 10.1088/1674-1137/35/6/004 shu
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Received: 2010-09-26
Revised: 2010-10-12
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Symmetries in a very special relativity and isometric group of Finsler space

Abstract: We present an explicit connection between the symmetries in a Very Special Relativity (VSR) and isometric group of a specific Finsler space. It is shown that the line element that is invariant under the VSR symmetric group is a Finslerian one. The Killing vectors in Finsler space are constructed in a systematic way. The Lie algebras corresponding to the symmetries of VSR are obtained from a geometric famework. The dispersion relation and the Lorentz invariance violation effect in the VSR are discussed.

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