Scalar and vector bosons in a Bonnor-Melvin-$\Lambda$ spacetime: an exact Duffin-Kemmer-Petiau analysis

Abstract

We study scalar and vector bosons in the Bonnor--Melvin--$\Lambda$ 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--$\Lambda$ 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.

20 pages, 4 figures

References in corpus (14)

• Quantum dynamics of scalar bosons in a cosmic string background
• Bonnor-Melvin universe with a cosmological constant
• Corroborating the equivalence between the Duffin-Kemmer-Petiau and the Klein-Gordon and Proca equations
• Relativistic spin-0 Duffin-Kemmer-Petiau equation in Bonnor-Melvin-Lambda solution
• Non-commutativity and non-inertial effects on a scalar field in a cosmic string space-time. Part 2: Spin-zero Duffin-Kemmer-Petiau-like oscillator
• DKP oscillator in the presence of a spinning cosmic string
• Aharonov-Bohm effect on the generalized Duffin-Kemmer-Petiau oscillator in the Som-Raychaudhuri space-time
• Charged scalar bosons in a Bonnor-Melvin-$\Lambda$ universe at conical approximation
• On the Klein-Gordon bosonic fields in the Bonnor-Melvin spacetime with a cosmological constant in rainbow gravity: Bonnor-Melvin Domain Walls
• Scalar bosons in Bonnor-Melvin-$\Lambda$ universe: Exact solution, Landau levels and Coulomb-like potential
• Klein-Gordon oscillator subject to a Coulomb-type potential in Bonnor-Melvin universe with a cosmological constant
• Klein-Gordon particles in a nonuniform external magnetic field in Bonnor-Melvin rainbow gravity background
• On the electromagnetic interaction and the anomalous term in the Duffin-Kemmer-Petiau theory
• Charged particle dynamics in singular spacetimes: hydrogenic mapping and curvature-corrected thermodynamics