Hamiltonian Formalism of the de-Sitter Invariant Special Relativity
Hamiltonian Formalism of the de-Sitter Invariant Special Relativity
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DOI：
10.1088/0253-6102/48/1/007
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发表时间：
2005-12
期刊：
影响因子：
--
通讯作者：
M. Yan;Neng-Chao Xiao;Wei Huang;Si Li
中科院分区：
文献类型：
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作者：
M. Yan;Neng-Chao Xiao;Wei Huang;Si Li
具有通用参数 $c$ ($\mathcal{SR}_c$) 的爱因斯坦狭义相对论的拉格朗日在庞加莱变换下保持不变，保留了洛伦兹度量 $\eta_{\mu\nu}$。 $\mathcal{SR}_c$ 已扩展为在 de Sitter 变换下不变的变量，保留了所谓的贝尔特拉米度量 $B_{\mu\nu}$。狭义相对论中有两个通用参数$c$和$R$（记为$\mathcal{SR}_{cR}$）。本文阐述了 $\mathcal{SR}_{cR}$ 的拉格朗日-哈密尔顿公式。导出了与时空德西特对称性相对应的正则能量、正则动量和10个诺特电荷。对$\mathcal{SR}_{cR}$无粒子的力学进行了规范量化。讨论了与之相关的物理学。
Lagrangian of the Einstein's special relativity with universal parameter $c$ ($\mathcal{SR}_c$) is invariant under Poincar\'e transformation which preserves Lorentz metric $\eta_{\mu\nu}$. The $\mathcal{SR}_c$ has been extended to be one which is invariant under de Sitter transformation that preserves so called Beltrami metric $B_{\mu\nu}$. There are two universal parameters $c$ and $R$ in this Special Relativity (denote it as $\mathcal{SR}_{cR}$). The Lagrangian-Hamiltonian formulism of $\mathcal{SR}_{cR}$ is formulated in this paper. The canonic energy, canonic momenta, and 10 Noether charges corresponding to the space-time's de Sitter symmetry are derived. The canonical quantization of the mechanics for $\mathcal{SR}_{cR}$-free particle is performed. The physics related to it is discussed.