Quantum dynamics of scalar particles in a spinning cosmic string background with topological defects: a Feshbach–Villars formalism perspective

Sarra Garah; Abdelmalek Boumali

doi:10.1140/epjc/s10052-025-14866-8

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2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2025) 85: 1257
https://doi.org/10.1140/epjc/s10052-025-14866-8

Regular Article - Theoretical Physics

Quantum dynamics of scalar particles in a spinning cosmic string background with topological defects: a Feshbach–Villars formalism perspective

Sarra Garah and Abdelmalek Boumali^a

Laboratory of Theoretical and Applied Physics, Echahid Cheikh Larbi Tebessi University, Tebessa, Algeria

^a boumali.abdelmalek@gmail.com

Received: 22 July 2025
Accepted: 27 September 2025
Published online: 5 November 2025

Abstract

We study the relativistic quantum dynamics of spin-0 particles in the spacetime of a spinning cosmic string that carries both spacelike disclination (conical deficit $α$ $\alpha$ ) and screw dislocation (torsion $J_{z}$ $J_{z}$ ) together with frame dragging ( $J_{t}$ $J_{t}$ ). Using the Feshbach–Villars (FV) reformulation of the Klein–Gordon equation, we obtain a first-order Hamiltonian with a positive-definite density, enabling a clean probabilistic interpretation for bosons in curved/topologically nontrivial backgrounds. In the weak-field regime (retaining terms $O (G)$ $\mathcal {O}(G)$ and discarding the $O (G^{2})$ $\mathcal {O}(G^{2})$ contribution that would otherwise lead to (double)-confluent Heun behavior), separation of variables in a finite cylinder of radius $R_{0}$ $R_{0}$ yields a Bessel radial equation with an effective index $ν (α, J_{t}, J_{z} ; E, k)$ $\nu (\alpha ,J_{t},J_{z};E,k)$ that mixes rotation and torsion. The hard-wall condition $J_{ν} (κ R_{0}) = 0$ $J_{\nu }(\kappa R_{0})=0$ quantizes the spectrum, $\begin{matrix} E_{n}^{2} = m^{2} + k^{2} + (j_{ν, n} / R_{0})^{2} . \end{matrix}$ $\begin{aligned} E_{n}^{2}=m^{2}+k^{2}+\big (j_{\nu ,n}/R_{0}\big )^{2}. \end{aligned}$ Working in the stationary positive-energy sector, we derive closed-form normalized eigenfunctions and FV densities, and we evaluate information-theoretic indicators (Fisher information and Shannon entropy) directly from the FV probability density. We find that increased effective confinement (via geometry/torsion) enhances Fisher information and reduces position-space Shannon entropy, quantitatively linking defect parameters to localization/complexity. The FV framework thus provides a robust, computationally transparent route to spectroscopy and information measures for scalar particles in rotating/torsional string backgrounds, and it smoothly reproduces the pure-rotation, pure-torsion, and flat-spacetime limits.

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Funded by SCOAP³.

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