TL;DR
This paper reviews various dynamical symmetries of the Dirac Hamiltonian, including relativistic spin, orbital angular momentum, and specific group symmetries, analyzing their conditions and deriving energy spectra using group theory.
Contribution
It systematically analyzes the conditions for dynamical symmetries in the Dirac Hamiltonian and derives energy spectra using group-theoretic methods.
Findings
Identifies conditions for relativistic spin and orbital symmetries.
Derives energy spectra for Dirac hydrogen atom and harmonic oscillator.
Establishes group-theoretic frameworks for these symmetries.
Abstract
Several dynamical symmetries of the Dirac Hamiltonian are reviewed in a systematic manner and the conditions under which such symmetries hold. These include relativistic spin and orbital angular momentum symmetries, SO(4)\times SU_{\sigma}(2) symmetry for the Dirac Hydrogen atom, SU(3)\times SU_{\sigma}(2) symmetry for the relativistic simple harmonic oscillator. The energy spectrum in each case is calculated from group-theoretic considerations.
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