arXiv subjects

Abdelmalek Boumali

Publications and source records attributed to Abdelmalek Boumali.

At least 19 recordsLinked to original sources

arXiv2026

Feshbach-Villars Formalism for a Spin-1/2 Particle in Curved Spacetime

This study explores the Feshbach-Villars (FV) formalism for spin-1/2 particles in curved spacetime. We derive the Hamiltonian form of the Dirac equation in this context and extend the FV transformation accordingly. The generalized Klein-Gordon equation, obtained by squaring the Dirac operator, is reformulated using the FV approach. We present the resulting Hamiltonian in both matrix and Pauli matrix forms, considering gravitational and electromagnetic interactions. The formalism is examined in both (1+2) and (1+3) dimensional spacetimes, with special attention given to the spin-field interaction term. This study provides a framework for studying relativistic quantum mechanics in curved spacetime, offering insights into the interplay between quantum effects, gravity, and electromagnetism.

hep-th↗

arXiv2026

Klein-Gordon Oscillator with Linear-Fractional Deformed Mass-Shell Invariants in Doubly Special Relativity

We study the Klein--Gordon (KG) oscillator in a doubly special relativity (DSR) framework, where the mass-shell condition is deformed through a linear--fractional (Möbius-type) modification of the Casimir invariant. This is induced by a nonlinear map from physical momenta $p^μ$ to auxiliary Lorentz-covariant variables $π^μ$. In $(1+1)$ dimensions, the deformation is controlled by a constant covector $a_μ$, yielding inequivalent realizations depending on whether $a_μ$ is timelike, spacelike, or lightlike. Implementing the KG oscillator via a reverted-product nonminimal coupling, we obtain exact closed-form spectra and explicit eigensolutions for both particle and antiparticle branches across all three geometries. Timelike and lightlike deformations produce identical spectra characterized by a Planck-suppressed additive displacement. This breaks the exact $E\leftrightarrow -E$ symmetry via a term linear in $E$, interpretable as a branch-independent reparametrization of the energy origin. Conversely, the spacelike deformation is strictly isospectral to the undeformed oscillator but generates complex-shifted wavefunctions and a non-Hermitian spatial operator. We provide a compact $\mathcal{PT}$-symmetric and pseudo-Hermitian formulation by constructing an explicit similarity map $\mathcal{S}$ to a Hermitian oscillator, deriving the metric operator $η=\mathcal{S}^\dagger \mathcal{S}$, and establishing biorthonormal relations. Finally, we compare quantitatively with the Magueijo--Smolin (DSR2) model: the squared-denominator invariant leads to a larger Planck-suppressed displacement at fixed $m/E_{Pl}$, highlighting the denominator power's role in controlling spectral shifts. Representative plots illustrate the dependence on deformation ratio, oscillator strength, and excitation level.

quant-ph↗

arXiv2026

Generalized Fock--Lorentz Transformations from Projective Conformal Coordinates: Covariant Structure, Sector Classification, and Oscillator Limits

We develop a covariant projective formulation of generalized Fock--Lorentz (GFL) transformations based on the auxiliary Minkowski coordinates $X^μ=x^μ/[1+a_νx^ν/R]$, where $R$ is a deformation length and $a^μ$ is a constant deformation vector. Ordinary Lorentz transformations acting linearly on $X^μ$ induce nonlinear transformations of the physical coordinates $x^μ$ with a unique denominator $\mathcal{D}_{a}(x;Λ)$ fixed by the conformal factor. The construction gives a unified invariant interval, clarifies the singular hypersurface of the projective chart, and separates three inequivalent sectors according to the causal character of $a^μ$: time-like, space-like, and null. We emphasize two points that are often obscured by analogy with the standard FL case: the coordinate velocity of light is generally defined by an implicit linear relation, and the familiar explicit FL expression is valid only in the purely time-like sector. The time-like apparent mass $m_{\rm app}(t)=m_{0}/(1+ct/R)$ and the associated one-dimensional Klein--Gordon and Dirac oscillator spectra are treated here only as limiting consistency checks of the generalized spacetime construction and are related explicitly to the companion momentum-space-dual formulation. The genuinely new dynamical result is obtained in the space-like sector, where the weak-gradient apparent mass generates a parity-breaking cubic anharmonicity; the first-order cubic shift vanishes by parity, while the combined second-order cubic and first-order quartic corrections yield a definite $R^{-2}$ shift of the oscillator operator. These results provide a transparent basis for future applications of projective relativistic kinematics without relying on a dark-universe interpretation.

physics.gen-ph↗

arXiv2026

Hyperstatistical thermodynamics of the one-dimensional Klein-Gordon and Dirac oscillators: a closed-form q-generalized Boltzmann factor and a quantitative comparison with Beck's superstatistics

We revisit the thermodynamics of the one-dimensional Klein-Gordon (KGO) and Dirac (DO) oscillators within two frameworks of generalized statistics: Beck's asymptotic superstatistics and the recently introduced hyperstatistics. In hyperstatistics, a $γ$-distribution of domain Boltzmann factors yields, after Laplace transformation and averaging over a normalisable density $f(β)$, the closed-form q-generalized Boltzmann factor $B_q(\varepsilon) = \exp_q(-\langleβ\rangle\varepsilon)$, independent of $f(β)$. We compute the partition function, entropy $S$, and specific heat $C_v$ for both 1D oscillators using excitation energies $\varepsilon_n = E_n - E_0$ to remove the rest-energy shift and enforce third-law behaviour $C_v \to 0$ as $T = 1/\langleβ\rangle \to 0$. Appropriate degeneracies ($g_n = 1$ for KGO; $g_0 = 1$, $g_n = 2$ for $n \geq 1$ for DO) are applied. Hyperstatistics successfully (i) reproduces the high-temperature Boltzmann limit $C_v \to 2k_B$, (ii) is structurally independent of $f(β)$, (iii) avoids the unphysical negative regions of the Beck polynomial bracket, and (iv) systematically distinguishes KGO from DO by capturing the enhanced entropy and sharper specific-heat structure caused by spin-induced degeneracy. The frameworks agree quantitatively for $q - 1 \ll 1$ and $\langleβ\rangle E \lesssim 2$, but diverge at high temperatures where Beck's polynomial expansion loses validity and the exact hyperstatistical q-exponential remains positive, monotonic, and analytic. Ultimately, hyperstatistics provides a numerically stable and analytically tractable alternative to asymptotic superstatistics for relativistic oscillators, naturally extensible to higher dimensions and external magnetic fields.

physics.gen-ph↗

arXiv2026

Klein--Gordon and Dirac Oscillators with an Apparent Mass Induced by the Momentum-Space Dual of the Fock--Lorentz Transformations

We propose a controlled momentum-space dual of the Fock--Lorentz (FL) transformations and use it to derive a deformed relativistic mass shell. Restricting the FL conformal factor to the cosmological-frame world line $\vx=0$, the invariant relation takes the form $(E^{2}-\vp^{2}c^{2})(1+ct/R)^{2}=m_{0}^{2}c^{4}$, which is equivalent to the standard special-relativistic dispersion law with a time-dependent apparent mass $\mapp(t)=m_{0}/(1+ct/R)$. Canonical quantization then yields Klein--Gordon (KG) and Dirac equations containing a slowly varying mass scale. We show explicitly that squaring the Dirac equation reproduces the KG operator, modulo first-order corrections proportional to $\dot\mapp$ that are suppressed by the ratio of the Compton wavelength to the FL scale. The construction is not presented as a unique covariant phase-space theory; rather, it is a world-line ansatz designed to isolate the spectral consequences of the FL conformal factor. As applications, we study the one-dimensional KG and Dirac oscillators. In the adiabatic regime, governed by the small parameter $ε=c/(Rω)\ll1$, closed-form instantaneous spectra are obtained. The Dirac-oscillator calculation is carried out in component form and then reduced to the physical spinor spectrum, thereby avoiding the double counting of the upper and lower component ladders. Dimensionless plots illustrate the apparent-mass drift, the induced spectral evolution, and the domain of adiabatic validity. For cosmological values of $R$, non-adiabatic corrections are entirely negligible; in the formal limit $t\to\infty$ the apparent mass tends to zero and, for fixed quantum number, the instantaneous levels collapse toward $E=0$.

physics.gen-ph↗

arXiv2026

Non-Abelian Dirac oscillator in a uniform Yang--Mills background: spin--isospin mixing and singlet--triplet splitting

We investigate a planar Dirac oscillator coupled to a spatially uniform $\utwo=\uone\times\su$ Yang--Mills background. The gauge configuration, adapted from the Dossa--Avossevou construction, contains an Abelian magnetic field $B$, a non-Abelian spatial amplitude $β$, and a non-Abelian scalar amplitude $ρ$. Within the Pauli-reduced formulation, the non-Abelian field strength produces a constant operator on $\mathbb{C}^{2}_{\mathrm{spin}}\otimes\mathbb{C}^{2}_{\mathrm{iso}}$. This operator contains a diagonal internal-Zeeman contribution proportional to $σ^{3}T^{3}$ and an off-diagonal spin--isospin term proportional to $σ^{1}T^{1}+σ^{2}T^{2}$. Its diagonalization gives a doubly degenerate aligned branch and two mixed branches with eigenvalues \[ λ_{\mathrm{FM}}=\frac{g^{2}β^{2}}{4m},\qquad λ_{S}=-\frac{g^{2}β(β-2ρ)}{4m},\qquad λ_{T}=-\frac{g^{2}β(β+2ρ)}{4m}. \] Consequently, the aligned internal-Zeeman scale is quadratic in $β$, whereas the singlet--triplet separation is linear in $βρ$. The revised formulation makes the sign conventions explicit, verifies the main limiting cases, distinguishes the Pauli-reduced spectrum from a full first-order Dirac diagonalization, and clarifies the physical meaning of the numerical illustrations.

hep-th↗

arXiv2026

Non-Extensive Generalization of Double Ionization by Electron Impact: Calculations of Both Cross Sections and Rate Coefficients for $\text{H}^-$, $\text{He}$, and $\text{Li}^+$

We generalize Tweed's seminal Born~I formalism for the electron-impact double ionization of two-electron atomic systems ($\text{H}^-$, $\text{He}$, $\text{Li}^+$) to non-extensive plasma environments described by Tsallis $q$-statistics. The bare Coulomb interaction is replaced by a $q$-deformed screened potential, which introduces a unique form factor envelope into the momentum-transfer integrations. We rederive the differential, partial, and total cross sections, demonstrating that this screening regularizes the classical high-energy Bethe logarithm and, in the $q < 1$ regime, induces diffraction-like oscillations in the angular cross sections. The model is calibrated against digitized historical experimental data to quantify how non-extensive screening deforms the vacuum baseline. Finally, coupling these cross sections to a $q$-Maxwellian distribution yields the macroscopic rate coefficients and reveals a novel subextensive critical-temperature threshold below which ionization is energetically forbidden.

physics.gen-ph↗

arXiv2026

Bounded thermal weights from a discrete Boltzmann factor

The discrete Boltzmann factor $B_E(β_n)=(1-bE)^n$, introduced by Chung, Hassanabadi, and Boumali, provides a lattice regularization of the canonical weight $e^{-βE}$ and imposes the compact-support condition $E<1/b$. In the present analysis we systematically separate results that follow directly from this bounded thermal weight from those that require additional phenomenological input. First, we study the discrete Bose--Einstein occupation factor relevant for Hawking radiation, derive the leading suppression of black-hole luminosity, and show that the thermal Hawking channel shuts off as the cutoff scale is approached. Second, we formulate a discrete work functional built from ratios of thermal weights and establish an exact Jarzynski-type identity for deterministic measure-preserving protocols; in contrast, the corresponding Crooks relation does not collapse to a function of work alone, and first-order approximations retain an explicit initial-energy dependence that cannot be reduced to a simple $W$-dependent correction without additional assumptions. Third, and purely as an ancillary kinematic extension rather than a derivation from the statistical framework itself, we examine a bounded modified-dispersion ansatz and estimate the associated time-of-flight constraints. Throughout, we include illustrative figures, clarify the non-universal status of the entropy correction, and emphasize that direct laboratory signatures are negligible whenever $b$ is universal and Planck suppressed. Finally, the standard continuum expressions are recovered smoothly in the limit $b\to 0$.

physics.gen-ph↗

arXiv2026

Electron-impact ionization rates for neutral He, Li, and Be in the Tsallis framework

The single-ionization rate coefficient of a plasma neutral depends both on the microscopic electron-impact cross section and on the macroscopic shape of the electron energy distribution function (EEDF). We present a reproducible benchmark and sensitivity study -- not a new theory -- of these two effects for the three lightest neutrals He, Li, and Be, combining the recommended Bell~\textit{et~al.}\ (1983) cross sections with a properly normalized two-temperature Tsallis $q$-generalized EEDF and varying $q$ on both sides of the Maxwellian limit and the hot-electron fraction $f_{\mathrm{hot}}$ at $T_{\mathrm{hot}}=10\,T_{\mathrm{bulk}}$. The calculation cleanly separates two independent uncertainty axes -- cross-section model (Bell vs.\ Lotz) and EEDF shape (Maxwellian vs.\ Tsallis). The Bell--Lotz spread on $τ_M$ is small for He (within about $7\%$), moderate for Be ($\lesssim 17\%$), and largest for Li (up to $+95\%$ at $T=1$~keV); sub-extensive distributions ($q<1$) suppress ionization through a hard tail cut-off, while super-extensive distributions ($q>1$) enhance low-temperature ionization through a $κ$-like power-law tail with $κ=1/(q-1)$. The quantitatively safest non-Maxwellian cases are $q=1$ and $q=1.2$ ($κ=5$), which lie inside the finite-mean-energy regime; the cases $q=1.4$ and $q=1.6$ are retained as heavy-tail stress tests and should be read as qualitative trends rather than as quantitatively reliable predictions. Both EEDF effects scale with $I_p/k_BT$, so He responds most strongly and Li least. The full numerical pipeline is released as a persistent reproducibility package, intended as a drop-in non-Maxwellian ionization module for collisional-radiative and ionization-balance modelling of light-neutral plasmas.

physics.gen-ph↗

arXiv2026

Non-Abelian Extensions of the Dirac Oscillator: A Theoretical Approach

We formulate the Dirac oscillator covariantly in the presence of external non-Abelian gauge fields. More precisely, the matter field is written as $Ψ_{αA}(x)$, where $α$ denotes the Dirac index and $A$ the isospin index, so that the Hamiltonian acts on the tensor-product space $\mathbb{C}^{4}\otimes\mathbb{C}^{2}$ in the fundamental representation. Starting from the gauge-covariant Dirac equation, we then implement the oscillator interaction through the standard non-minimal substitution and promote the construction to an $\mathrm{SU}(2)$ background. In this way, we derive the associated non-Abelian field-strength tensor and isolate the commutator contribution, which has no Abelian analogue. Consequently, the generalized Pauli interaction $σ^{μν}\mathcal{F}_{μν}$ produces matrix-valued spin--isospin couplings. At the same time, the Abelian sector reduces to the conventional Moshinsky--Szczepaniak Dirac oscillator, whose exactly solvable spectrum provides a natural benchmark for the extended theory.

quant-ph↗

arXiv2026

Black-hole thermodynamics in doubly special relativity: near-horizon g/f temperature scaling under a shared operational scale

Doubly Special Relativity (DSR) deforms special-relativistic kinematics by introducing an invariant Planck energy scale $E_{\mathrm{Pl}}$ alongside the speed of light, while preserving the relativity principle. A key issue in curved spacetimes, particularly black-hole thermodynamics, is the operational meaning of the ``energy'' in modified dispersion relations (MDRs). We compare two common implementations in a controlled static black-hole spacetime: (i) MDRs in local orthonormal frames on a fixed background geometry, and (ii) the rainbow-metric approach with an energy-dependent family of effective metrics. For static, spherically symmetric horizons and using a consistent finite operational energy scale $E_\star$ for emitted quanta, both yield the same near-horizon temperature rescaling \[ T(E_\star)=T_0\,\frac{g(E_\star/E_{\mathrm{Pl}})}{f(E_\star/E_{\mathrm{Pl}})}, \quad T_0=κ_0/(2π), \] where $f$ and $g$ are the standard rainbow/MDR functions. This establishes a universality of the tunneling/surface-gravity temperature, with deformation entering solely via the ratio $g/f$. We illustrate for Amelino-Camelia MDR and Magueijo-Smolin DSR (where $f=g$, implying $T(E_\star)=T_0$). Extending to a two-parameter generalized DSR (G-DSR) with leading parameters $(α_2, Δα)$, we obtain \[ T_{\mathrm{GDRS}}(E_\star) = T_0 \sqrt{\frac{1-2Δα\,(E_\star/E_{\mathrm{Pl}})}{1-2α_2\,(E_\star/E_{\mathrm{Pl}})}} \simeq T_0 [1 - (Δα- α_2) E_\star/E_{\mathrm{Pl}}]. \] We discuss the role of $Δα- α_2$ (vanishing correction for the symmetric $Δα=α_2$ subfamily) and note that further model dependence arises from phase-space measures, greybody factors, and non-linear composition laws. Corrections are strongly suppressed for macroscopic black holes and become relevant only near the Planck regime.

gr-qc↗

arXiv2026

Analytical Solutions of One-Dimensional ($1\mathcal{D}$) Potentials for Spin-0 Particles via the Feshbach-Villars Formalism

We present a unified analytical and numerical study of the one-dimensional Feshbach--Villars (FV) equation for spin-0 particles in the presence of several representative external potentials. Starting from the FV formulation of the Klein--Gordon equation, we derive the corresponding one-dimensional master equation and analyse its solutions for Coulomb, power-exponential, Cornell, Pöschl--Teller, and Woods--Saxon interactions. For the singular Coulomb and Cornell cases, a Loudon-type cutoff regularisation is implemented on the full line, allowing a mathematically controlled treatment of the origin and an explicit classification of the states by parity. The Coulomb problem exhibits the expected near-degenerate even--odd structure in the cutoff limit, while the Cornell potential combines short-distance Coulomb behaviour with long-distance confinement and produces a finite set of bound states for fixed parameters. The power-exponential potential with $p=1$ is reduced to a Whittaker-type equation and yields an intrinsically relativistic spectrum with no standard Schrödinger bound-state limit in the parameter regime considered. For the smooth short-range Pöschl--Teller and Woods-Saxon potentials, the FV formalism reveals, respectively, the effects of definite parity and spatial asymmetry on the spectrum, wave functions, and particle--antiparticle mixing. In all cases, we reconstruct the full FV spinor, analyse the associated charge density, and compare the relativistic behaviour with the corresponding non-relativistic expectations whenever such a limit exists. The results provide a coherent set of analytical and numerical benchmarks for relativistic scalar bound states in one dimension.

quant-ph↗

arXiv2026

Nonlocal Generalized Dirac Oscillators in (1 + 1) Dimensions

We propose a nonlocal extension of the generalized Dirac oscillator (GDO) in $(1+1)$ dimensions by replacing the multiplicative interaction $f(x)$ with an integral operator $\hat F$ with kernel $f(x,x')$. The resulting Dirac equation preserves an operator factorization and decouples into two nonlocal Schrödinger-type (Sturm--Liouville) equations for the spinor components. We derive explicit expressions for the associated supersymmetric partner kernels in terms of $f$ and its derivatives, and we show that a complex-translation metric $η=e^{-θp_x}$ leads to a simple sufficient \emph{kernel-level} pseudo-Hermiticity constraint, $f(x+\ii\hbarθ,x'+\ii\hbarθ)=f^*(x',x)$, extending the familiar local complex-shift criteria. To provide a transparent \emph{nonlocal-to-local} interpretation, we adapt the Coz--Arnold--MacKellar current-based localization to each component equation, obtaining energy-dependent equivalent local potentials and multiplicative Perey (damping) factors. The mapping breaks down precisely at current zeros, thereby diagnosing the spurious solutions of the corresponding nonlocal Schrödinger problem. Finally, we illustrate the formalism with analytically tractable benchmarks (the local Dirac oscillator and a translation-invariant kernel) and with a finite-rank separable model (Gaussian form factor) that reduces the integro-differential problem to a small set of coupled ordinary differential equations and algebraic constraints.

quant-ph↗

arXiv2026

The Generalized Dirac Oscillator in Doubly Special Relativity: A Complexified Morse Interaction

We study the one-dimensional Generalized Dirac Oscillator (GDO) under Doubly Special Relativity (DSR) kinematics. The GDO extends the Dirac oscillator by replacing the linear non-minimal coupling with a general interaction function $f(x)$, thereby generating broad families of exactly solvable relativistic models and, for suitable complex choices of $f(x)$, entering the domain of $η$-pseudo-Hermitian and $\mathcal{PT}$-symmetric dynamics with real spectra. We present a review of the factorization (supersymmetric) structure that decouples the GDO into partner Schrödinger-like Hamiltonians, and we clarify how pseudo-Hermiticity and $\mathcal{PT}$ symmetry provide consistent inner products and reality conditions for the spatial spectrum. We then embed these results into two representative DSR prescriptions: the Magueijo--Smolin (MS) and the Amelino--Camelia (AC) frameworks. In this approach, the spatial problem yields a real set $\{ε_n\}$, while DSR deforms the algebraic reconstruction map between $ε_n$ and the relativistic energies $E_n$. The MS model induces a branch-asymmetric deformation through an energy-dependent effective mass, whereas the AC model introduces a characteristic criticality through a momentum-sector deformation, resulting in an admissibility requirement of the form $ε_n<4k^2$ in the leading-order realization adopted here. As an explicit illustration, we treat a pseudo-Hermitian complexified Morse interaction, discuss the interplay between the intrinsic Morse finiteness of bound states and DSR-induced truncations, and analyze the massless limit ($m=0$), where MS collapses to the undeformed energy map while AC remains deformed.

hep-th↗

arXiv2026

The Generalized Klein--Gordon Oscillator in Doubly Special Relativity: A Complexified Morse Interaction

We investigate the one-dimensional \emph{Generalized Klein--Gordon Oscillator} (G-KGO) within Doubly Special Relativity (DSR) kinematics. The G-KGO extends the Klein--Gordon oscillator by replacing the usual linear non-minimal coupling with a general interaction function $f(x)$, leading to a factorized (SUSY-like) Schrödinger operator $H_-=\mathcal{A}^{\#}\mathcal{A}$ whose real spatial spectrum $\{ε_n\}$ can be ensured either by Hermiticity or, for complex $f(x)$, by $η$-pseudo-Hermiticity and/or $\mathcal{PT}$ symmetry with a consistent metric inner product \cite{Bender1998,Bender2007RPP,BBJ2002PRL,Mostafazadeh2002,Mostafazadeh2003,Mostafazadeh2010,ElGanainy2018NatPhys}. DSR is then implemented at the level of the energy reconstruction map $ε_n\mapsto E_{n,\pm}$, and we provide closed-form Magueijo--Smolin (MS) and Amelino--Camelia (AC) branches.

hep-th↗

arXiv2026

Three-Dimensional Modified Klein--Gordon Oscillator in Standard and Generalized Doubly Special Relativity

Doubly Special Relativity (DSR) augments special relativity by introducing, alongside the invariant speed of light $c$, a second observer-independent scale typically associated with the Planck regime. At the level of effective wave equations this principle manifests itself through deformed dispersion relations and energy-dependent spatial operators. Here we quantify such effects in a prototypical exactly solvable bound-state problem: the three-dimensional Klein--Gordon oscillator generated by a non-minimal momentum coupling that yields isotropic harmonic confinement while preserving rotational symmetry. We analyze two standard DSR realizations (Amelino--Camelia and Magueijo--Smolin, parametrized by an invariant energy scale $k$) as well as a generalized DSR framework based on a first-order expansion in the Planck length $l_p$. After stationary reduction and separation in spherical coordinates, the eigenfunctions retain the generalized-Laguerre and spherical-harmonic structure of the undeformed oscillator, whereas DSR deforms the algebraic quantization condition that relates the principal oscillator number $N=2n+\ell\in\mathbb{N}_0$ to the relativistic energy. Closed-form spectra are obtained for the standard DSR cases, and perturbative Planck-suppressed shifts are derived for the generalized model. In all realizations the deformation induces branch-dependent shifts of both positive- and negative-energy solutions, which increase with excitation and vanish smoothly in the limits $k\to\infty$ or $l_p\to0$. The main goal of this paper is to extract analytic spectra and Planck-suppressed shifts that enable a direct comparison between different DSR prescriptions in a fully three-dimensional setting.

hep-th↗

arXiv2026

Three-Dimensional Modified Dirac Oscillator in Standard and Generalized Doubly Special Relativity

% Doubly Special Relativity (DSR) introduces, besides the invariant speed of light $c$, an observer-independent high-energy % scale that deforms relativistic kinematics and can be implemented through modified dispersion relations or effective % wave equations with energy-dependent spatial operators. In this work we develop a three-dimensional, exactly solvable % benchmark for such deformations in the spin-$\tfrac12$ sector: the Dirac oscillator. Following the original % construction of Moshinsky and Szczepaniak, the oscillator is introduced through a linear non-minimal momentum coupling, % which preserves Hermiticity and yields, after decoupling the Dirac equation into large and small components, a % three-dimensional isotropic harmonic-oscillator operator supplemented by a strong spin--orbit term. % We then incorporate Planck-scale deformations in two standard DSR realizations (Amelino--Camelia and % Magueijo--Smolin, characterized by an invariant energy scale $k$) and in a generalized DSR framework based on a % first-order expansion in the Planck length $l_p$. In all cases the bound-state eigenfunctions retain the % oscillator-spinor structure dictated by spherical symmetry, while DSR deforms the algebraic relation between quantum % numbers $(N,j,\ell)$ and the relativistic energy, producing branch-dependent shifts for both particle and antiparticle % solutions. The undeformed limit ($k\to\infty$ or $l_p\to0$) is recovered smoothly and the deformation signal increases % with excitation through the oscillator scale and spin--orbit splitting.

physics.gen-ph↗

arXiv2025

Analysis of Spin-1/2 Particle Scattering in a Spinning Cosmic String Spacetime with Torsion, Curvature, and a Coulomb Potential

This paper investigates the scattering states of spin-1/2 particles in the spacetime of a spinning cosmic string with spacelike disclination and dislocation, with and without a Coulomb interaction. Working within the tetrad formalism, we solve the Dirac equation for several configurations of the angular momentum density $J_t$ and the torsion parameter $J_z$ that are relevant from a physical perspective. These configurations include balanced torsion ($J_t = J_z$), pure spinning strings ($J_z = 0$), pure screw dislocations ($J_t = 0$) and the general case. In all cases, the geometry modifies an effective azimuthal quantum number, and for strong rotation it introduces a geometric radial cutoff $ρ_c$ that acts as a hard wall. These factors lead to closed-form expressions for the radial wave functions, phase shifts and differential cross sections, which are expressed in terms of confluent hypergeometric and Bessel functions. We demonstrate that conical curvature, rotation and torsion generate Aharonov-Bohm-like contributions, as well as energy- and momentum-dependent asymmetries in Dirac-Coulomb scattering. This results in topology-renormalised Mott/Rutherford patterns. In the Coulomb-free limit, scattering becomes purely geometric yet still exhibits characteristic forward enhancement, which is governed by defect parameters and the cutoff. We briefly discuss possible realisations in Dirac materials, such as strained or defective graphene, where lattice disclinations and dislocations mimic the cosmic-string geometry.

hep-th↗