Hamiltonian Formalism of the de-Sitter Invariant Special Relativity

TL;DR

This paper develops a Hamiltonian formalism for de Sitter invariant special relativity with two universal parameters, deriving conserved charges and quantization, extending the classical framework of special relativity.

Contribution

It introduces a Hamiltonian formulation of de Sitter invariant special relativity with two parameters, including conserved charges and quantization methods.

Findings

Derived canonical energy, momenta, and Noether charges.

Formulated Hamiltonian mechanics for de Sitter invariant relativity.

Performed canonical quantization of free particle mechanics.

Abstract

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.