Quantum Dynamics of Scalar Particles in a Spinning Cosmic String Background with Topological Defects: A Feshbach-Villars Formalism Perspective

TL;DR

Addressing the relativistic quantum dynamics of spin-0 particles in the spacetime of a spinning cosmic string with conical deficit $\alpha$, screw dislocation $J_z$, and frame dragging $J_t$, the paper adopts the Feshbach–Villars formalism to obtain a first-order Hamiltonian with a positive-definite density. The radial problem, analyzed in a weak-field Dirichlet cylinder, reduces to a Bessel equation with an effective order $\nu(\alpha,J_t,J_z;E,k)$ and yields a discrete spectrum $E_n^2 = m^2 + k^2 + (j_{\nu,n}/R_0)^2$. The FV density is positive-definite, enabling direct computation of information-theoretic quantities such as Fisher information $I_r$ and Shannon entropy $S_r$, which reveal increased localization with stronger confinement and larger $n$. The work recovers pure-rotation, pure-torsion, and flat-space limits and highlights the FV framework as a transparent route to scalar spectroscopy and information measures in curved, topologically nontrivial backgrounds.

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 $α$) and screw dislocation (torsion $J_z$), as well as frame dragging ($J_t$). 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 or topologically nontrivial backgrounds. In the weak-field regime (retaining terms $\mathcal{O}(G)$ and discarding the $\mathcal{O}(G^2)$ contribution that would otherwise lead to double-confluent Heun behavior), separation of variables in a finite cylinder of radius $R_0$ yields a Bessel radial equation with an effective index $ν(α, J_t, J_z; E, k)$ that mixes rotation and torsion. The hard-wall condition $J_ν(κR_0) = 0$ quantizes the spectrum, $E_n^2 = m^2 + k^2 + \left(\frac{j_{ν,n}}{R_0}\right)^2$. Working in the stationary positive-energy sector, we derive closed-form normalized eigenfunctions and FV density, 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 localisation/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.

Figures (4)

• Figure 1: Discrete eigen-energies $E_{n}$ plotted against the radial quantum number $n$ for several values of the effective angular momentum $\ell_{\text{eff}}$ in the spacetime of a spinning cosmic string with torsion.
• Figure 2: Positive-definite Feshbach--Villars probability density $\rho_{\text{FVO}}(r)$ for low-lying states ($n=0\!-\!5$) at different $\ell_{\text{eff}}$, showing how torsion and rotation shift the spatial localization of the wave-function.
• Figure 3: Variation of the Fisher information $I_{F}$ with radial quantum number $n$ for several $\ell_{\text{eff}}$; higher $I_{F}$ at large $n$ indicates increasing localization of the scalar particle in the defect space--time.
• Figure 4: Shannon entropy $S$ as a function of $n$ for different $\ell_{\text{eff}}$; the declining trend reflects the reduction in configurational complexity as the states become more localized.