邦诺 - 梅尔文 - Λ时空中的标量和矢量玻色子：精确的达芬 - 凯默 - 佩蒂奥分析
Scalar and vector bosons in a Bonnor-Melvin-$Λ$ spacetime: an exact Duffin-Kemmer-Petiau analysis
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中文总结 AI 辅助
研究邦诺 - 梅尔文 - Λ时空中标量和矢量玻色子，借助梅泽瓦投影算符在全弯曲时空导出精确二阶方程，不依赖圆锥近似，得到各部分离散径向谱及本征函数，统一精确处理并补充先前分析，阐明背景几何结构作用。
中文摘要 AI 辅助
我们在达芬 - 凯默 - 佩蒂奥（DKP）形式体系下研究邦诺 - 梅尔文 - Λ时空中的标量和矢量玻色子。通过使用梅泽瓦投影算符，分离出物理自旋 - 0 和自旋 - 1 部分，在全弯曲时空中导出相应的精确二阶方程，不依赖于圆锥近似。标量部分的径向方程简化为具有三角普施尔 - 特勒有效势的类似薛定谔方程。矢量部分，纵向模式由相同有效势支配，横向极化由广义三角普施尔 - 特勒势描述。由于度规函数在离散径向点处消失，径向动力学自然地表述为基本区间上的奇异斯特姆 - 刘维尔问题，物理径向域由相应奇异径向算符的弗里德里希斯自伴延拓确定。结果，所有物理部分都呈现纯离散径向谱，且其本征函数以封闭形式获得。这些结果提供了对邦诺 - 梅尔文 - Λ时空中标量和矢量玻色子的统一精确处理，补充了基于圆锥近似的先前分析，并阐明了背景全局几何结构在形成禁闭和谱性质中的作用。
英文摘要
We study scalar and vector bosons in the Bonnor--Melvin--$Λ$ 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--$Λ$ 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.
