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arXiv:2511.19748

Exact Solutions for the Kemmer Oscillator in 1+1 Rindler Coordinates

T. Rouabhia, A. Boumali

gr-qcquant-phSubmitted Nov 24, 2025• Announced Nov 26, 2025
arXivHTMLPDF

Abstract

This work presents exact solutions of the Kemmer equation for spin-1 particles in $(1+1)$-dimensional Rindler spacetime, motivated by the need to understand vector bosons under uniform acceleration, including non-inertial effects and the Unruh temperature, which distinguish them from spin-0 and spin-1/2 systems. Starting from the free Kemmer field in an accelerated reference frame, we establish eigenvalue equations resembling those of the Klein--Gordon equation in Rindler coordinates. By introducing the Dirac oscillator interaction through a momentum substitution, we derive an exact closed-form spectrum for the Kemmer oscillator, revealing how the acceleration parameter modifies the characteristic length, shifts the discrete energy spectrum, and lifts degeneracies. In the Minkowski limit $a\to 0$, the standard Kemmer oscillator spectrum is recovered, ensuring consistency with flat-spacetime results. These findings provide a tractable framework for analyzing acceleration-induced effects, with implications for quantum field theory in curved spacetime, quantum gravity, and analogue gravity platforms.

Comments
This paper has been accepted for publication In Ukranian Journal of Physics

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This work presents exact solutions of the Kemmer equation for spin-1 particles in (1+1)(1+1)(1+1)-dimensional Rindler spacetime, motivated by the need to understand vector bosons under uniform acceleration, including non-inertial effects and the Unruh temperature, which distinguish them from spin-0 and spin-1/2 systems. Starting from the free Kemmer field in an accelerated reference frame, we establish eigenvalue equations resembling those of the Klein--Gordon equation in Rindler coordinates. By introducing the Dirac oscillator interaction through a momentum substitution, we derive an exact closed-form spectrum for the Kemmer oscillator, revealing how the acceleration parameter modifies the characteristic length, shifts the discrete energy spectrum, and lifts degeneracies. In the Minkowski limit a→0a\to 0a→0, the standard Kemmer oscillator spectrum is recovered, ensuring consistency with flat-spacetime results. These findings provide a tractable framework for analyzing acceleration-induced effects, with implications for quantum field theory in curved spacetime, quantum gravity, and analogue gravity platforms.
Spin-0 and Spin-1 Bosonic Particles Dynamics in (1+3)(1+3)(1+3) Dimensions via the Relativistic DKP Equation with a Spatially-Dependent Exponential Mass Term
Abstract The Duffin-Kemmer-Petiau (DKP) equation is a relativistic wave equation governing the dynamics of spin-0 and spin-1 bosonic particles. In this work, we study the (1+3)(1+3)(1+3) ( 1 + 3 ) -dimensional DKP equation with a spatially dependent mass under a modified deformed exponential type potential. Using the framework of supersymmetric quantum mechanics, we derive approximate analytical solutions. A novel extension of the Pekeris approximation is introduced to treat the centrifugal barrier, enabling the complete determination of the energy spectrum. The non-relativistic limit of the DKP equation is obtained via an established transformation technique. The model is applied to diatomic molecules including lithium hydride (LiH), hydrogen chloride (HCl), 7Li2^{7}\textrm{Li}_{2}7Li2​ 7 Li 2 , Na2\textrm{Na}_{2}Na2​ Na 2 , and ScI. The energy spectra are computed for various quantum states ∣n,l,j⟩\left| n,l,j\right\rangle ∣n,l,j⟩ n , l , j using both relativistic and non-relativistic expressions. For LiH and HCl, where experimental data are scarce, our results show strong agreement with earlier theoretical predictions. For 7Li2^{7}\textrm{Li}_{2}7Li2​ 7 Li 2 , Na2\textrm{Na}_{2}Na2​ Na 2 , and ScI, the calculated energies align excellently with available experimental data. The proposed framework provides a reliable and analytically tractable tool for studying bosonic systems with position-dependent effective masses.
A uniformly accelerated observer perceives the Minkowski vacuum as a thermal bath, so acceleration acts as a noise channel on correlations shared with an inertial partner. For a Dirac field in the standard treatment, the resulting map is a one-sided amplitude-damping channel, and entanglement and quantum discord survive at infinite acceleration. We introduce a symmetric Unruh-like map in which the vacuum and the one-particle state both exchange amplitude with the inaccessible Rindler region; for a Bell state it yields a bit-flip channel whose flip probability is the Fermi-Dirac occupation at the Unruh temperature. Using negativity, mutual information, and all six pairwise quantum discords, we find that the entanglement and discord between the inertial observer and the accessible mode vanish together at infinite acceleration, leaving only one bit of classical correlation. These results show that the fate of quantum correlations in noninertial frames depends on the structure of the Minkowski-Rindler map.
While the Unruh effect has traditionally been studied under the assumption of uniform acceleration, a simplification motivated by experimental considerations, it is not necessarily true for all non-inertial motions. We propose a novel approach for the indirect detection of the Unruh effect without relying on the former restriction. Previous studies have shown that probing the decoherence of an Unruh-DeWitt detector can significantly reduce the acceleration required for observing the effect by several orders of magnitude compared to earlier proposals. Building on this idea, we develop a theoretical framework describing a non-inertial observer equipped with a detector undergoing non-uniform, time-dependent acceleration. We show that, in a non-uniformly accelerated Rindler spacetime, the particle distribution perceived in the Minkowski vacuum acquires a time-dependent modification of the standard Unruh spectrum. Furthermore, we demonstrate that the inclusion of quantum entanglement leads to a deformation of the Minkowski vacuum into squeezed states.
Scalar and vector bosons in a Bonnor-Melvin-ΛΛΛ spacetime: an exact Duffin-Kemmer-Petiau analysis
We study scalar and vector bosons in the Bonnor--Melvin--ΛΛΛ spacetime within the Duffin--Kemmer--Petiau (DKP) formalism. By employing Umezawa's projection operators, we separate the physical spin-0 and spin-1 sectors and derive the corresponding exact second-order equations in the full curved spacetime, without relying on the conical approximation. For the scalar sector, the radial equation reduces to a Schrödinger-like equation with a trigonometric Pöschl--Teller effective potential. In the vector sector, the longitudinal mode is governed by the same effective potential, whereas the transverse polarizations are described by generalized trigonometric Pöschl--Teller potentials. Because the me\-tric function vanishes at a discrete set of radial points, the radial dynamics is naturally formulated as a singular Sturm--Liouville problem on a fundamental interval, with the physical radial domain fixed by the Friedrichs self-adjoint extension of the corresponding singular radial operators. As a result, all physical sectors exhibit purely discrete radial spectra, and their eigenfunctions are obtained in closed form. These results provide a unified exact treatment of scalar and vector bosons in the Bonnor--Melvin--ΛΛΛ spacetime, complement previous analyses based on the conical approximation, and clarify the role of the global geometric structure of the background in shaping confinement and spectral properties.
Abstract Non-inertial physics is seldom considered in quantum mechanics and this contrasts with the ubiquity of non-inertial reference frames. Here, we show an application to the Dirac oscillator which provides a fundamental model of relativistic quantum mechanics. The model emerges from a term linearly dependent on spatial coordinates added to the momentum of the free-particle Dirac Hamiltonian. The definition generates peculiar features (mutating vacuum energy, non-Hermitian momentum, accidental degeneracies of the spectrum, etc). We interpret these anomalies in terms of inertial effects. The demonstration is based on the decoupling of the Dirac equation from the stereographic projection that maps the 3D geometry of the dynamical problem to the complex plane. The decoupling shows that the fundamental mechanical model underpinning the Dirac oscillator reduces to the representation of the oscillator in the rotating reference frame attached to the orbital angular momentum. The resulting Coriolis-like contribution to the Hamiltonian accounts for the peculiarities of the model (mutating vacuum energy, form of the non-minimal correction to the momentum, classical intrinsic spin and gain of its quantum value, accidental degeneracies of the energy spectrum, supersymmetric potential). The suggested interpretation has an interdisciplinary character where stereographic geometry, classical physics of the Coriolis effect and quantum physics of Dirac particles contribute to the definition of one of the few exactly soluble models of relativistic quantum mechanics.
Exact Solution of the (2+1)(2+1)(2+1)-Dimensional Dunkl-Klein-Gordon Oscillator with a Uniform Magnetic Field in Non-Commutative Phase Space
We solve the Klein-Gordon oscillator in a non-commutative phase space, generalized using Dunkl derivatives, both with and without interaction with a uniform magnetic field. For each of these cases, we begin by introducing the Dunkl derivative into the standard commutative phase space to evaluate the reflection parity symmetries. Then, using the Seiberg-Witten map, we extend the generalized system to a non-commutative phase space. In both cases, we determine the eigenfunctions and the energy spectrum exactly (which correspond to generalized Landau levels when a magnetic field is present). Furthermore, we compute the non-relativistic limit of the system and graphically analyze the behavior of the energy spectra. Our results demonstrate that the combination of the Dunkl deformation parameters, the non-commutative phase space geometry, and the magnetic field produces a parity-dependent modification of the energy levels. Finally, we verify that when the external magnetic field or the non-commutative parameters vanish, our exact solutions correctly reduce to the commutative Dunkl models established in previous works.