An algebraic solution of Dirac equation on a static curved space-time

TL;DR

This paper derives exact solutions to the Dirac equation in static curved space-time using algebraic methods, specifically $su(1,1)$ algebra, for various potentials including hydrogen and Morse oscillators.

Contribution

It introduces two algebraic approaches to solve the Dirac equation in curved space-time, extending the analysis to multiple potentials and deriving energy spectra and eigenfunctions.

Findings

Exact solutions for hydrogen and Morse oscillator in curved space-time

Both methods produce $su(1,1)$ algebraic structures leading to energy spectra

Extension to linear radial potential with consistent algebraic framework

Abstract

We present exact solutions of the Dirac equation in static curved space-time using two distinct algebraic approaches. The first method employs $su(1,1)$ algebra operators together with the tilting transformation, enabling the derivation of the energy spectrum and eigenfunctions for both the Hydrogen atom and the Dirac-Morse oscillator. The second approach, based on the Schr\"odinger factorization method, extends the analysis to three representative potentials: the hydrogen atom, the Dirac-Morse oscillator, and a linear radial potential. Although structurally different from those obtained in the first method, the resulting operators in this approach also close the $su(1,1)$ algebra and, through representation theory, yield the corresponding energy spectra and eigenfunctions.