Hamiltonian Formalism of the de-Sitter Invariant Special Relativity

Abstract

Lagrangian of the Einstein's special relativity with universal parameter $c$ (${\mathcal{S}\mathcal{R}}_c$) is invariant under Poincaré transformation which preserves Lorentz metric ${\eta }_{\mu \nu }$. The ${\mathcal{S}\mathcal{R}}_c$ 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 ${\mathcal{S}\mathcal{R}}_{cR}$). The Lagrangian-Hamiltonian formulism of ${\mathcal{S}\mathcal{R}}_{cR}$ 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 ${\mathcal{S}\mathcal{R}}_{cR}$-free particle is performed. The physics related to it is discussed.

24 pages, no figure

References in corpus (4)

• On Special Relativity with Cosmological Constant
• On Beltrami Model of de Sitter Spacetime
• Mechanics and Newton-Cartan-Like Gravity on the Newton-Hooke Space-time
• Three Kinds of Special Relativity via Inverse Wick Rotation

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