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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2601.18836 |
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| _version_ | 1866910001695555584 |
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| author | Boumali, A. Jafari, N. Chargui, Y. |
| author_facet | Boumali, A. Jafari, N. Chargui, Y. |
| contents | We develop a first-order Feshbach-Villars (FV) Hamiltonian framework for spin-0 relativistic quantum dynamics in the presence of Planck-scale kinematic deformations described within generalized doubly special relativity (G-DSR). Starting from a generic nonlinear momentum-space map, we derive the corresponding modified dispersion relation (MDR) at leading order in the Planck length \(l_p\) and construct a consistent FV linearization of the deformed Klein-Gordon operator. The resulting two-component Hamiltonian remains \(σ_3\)-pseudo-Hermitian at \(\mathcal{O}(l_p)\), which guarantees conservation of the FV charge and current and provides a current-based definition of reflection and transmission in stationary scattering.
As applications, we study two benchmark settings in which the FV metric structure is essential: (i) the one-dimensional Klein-Gordon oscillator and (ii) scattering from electrostatic step and barrier potentials. For the oscillator, we obtain controlled \(\mathcal{O}(l_p)\) branch-resolved spectral shifts and show how kinetic versus mass-shell deformations reshape the level spacing and the high-energy spectral compression. For step and barrier scattering, we compute reflection and transmission coefficients directly from the pseudo-Hermitian FV current and quantify the deformation-induced shift of the supercritical (pair-production) threshold. A comparative analysis of the Amelino-Camelia and Magueijo-Smolin realizations indicates that MS-type deformations generally delay the onset of the supercritical regime and reduce the magnitude of the negative transmitted flux within the validity domain \(l_p E \ll 1\). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18836 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Feshbach-Villars Hamiltonian Approach to the Klein-Gordon Oscillator and Supercritical Step Scattering in Standard and Generalized Doubly Special Relativity Boumali, A. Jafari, N. Chargui, Y. Quantum Physics General Relativity and Quantum Cosmology High Energy Physics - Theory We develop a first-order Feshbach-Villars (FV) Hamiltonian framework for spin-0 relativistic quantum dynamics in the presence of Planck-scale kinematic deformations described within generalized doubly special relativity (G-DSR). Starting from a generic nonlinear momentum-space map, we derive the corresponding modified dispersion relation (MDR) at leading order in the Planck length \(l_p\) and construct a consistent FV linearization of the deformed Klein-Gordon operator. The resulting two-component Hamiltonian remains \(σ_3\)-pseudo-Hermitian at \(\mathcal{O}(l_p)\), which guarantees conservation of the FV charge and current and provides a current-based definition of reflection and transmission in stationary scattering. As applications, we study two benchmark settings in which the FV metric structure is essential: (i) the one-dimensional Klein-Gordon oscillator and (ii) scattering from electrostatic step and barrier potentials. For the oscillator, we obtain controlled \(\mathcal{O}(l_p)\) branch-resolved spectral shifts and show how kinetic versus mass-shell deformations reshape the level spacing and the high-energy spectral compression. For step and barrier scattering, we compute reflection and transmission coefficients directly from the pseudo-Hermitian FV current and quantify the deformation-induced shift of the supercritical (pair-production) threshold. A comparative analysis of the Amelino-Camelia and Magueijo-Smolin realizations indicates that MS-type deformations generally delay the onset of the supercritical regime and reduce the magnitude of the negative transmitted flux within the validity domain \(l_p E \ll 1\). |
| title | Feshbach-Villars Hamiltonian Approach to the Klein-Gordon Oscillator and Supercritical Step Scattering in Standard and Generalized Doubly Special Relativity |
| topic | Quantum Physics General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2601.18836 |