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arXiv · 2505.08726

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

M. Salazar-Ramíreza·R. D. Motab·D. Ojeda-Guillén·A. González-Cisneros
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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.

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M. Salazar-Ramíreza, R. D. Motab, D. Ojeda-Guillén, A. González-Cisneros. 2025-05-13. An algebraic solution of Dirac equation on a static curved space-time. https://arxiv.org/abs/2505.08726

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