发表机构
Islamic Azad University, Qazvin（伊斯兰阿扎德大学（加兹温））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出三层味中微子在分层非均匀物质中传播时开放路径几何相位的规范不变形式体系，阐明其非对易味演化特性，揭示Dirac CP相位的影响及几何相位通过干涉贡献跃迁概率的唯象学意义。
AI 中文摘要
我们提出了在非均匀物质中传播的三层味中微子振荡语境下开放路径几何相位的规范不变表述。与本质上关联闭合绝热循环的标准Berry相位不同，中微子从源到探测器的传播通常在依赖物质的哈密顿量参数空间中描绘出一条开放轨迹。我们在分层物质框架内推导了该形式体系，其中每个离散层具有恒定密度和局域物质本征基。总演化算子表示为动力学传播因子与连接相邻物质本征基的界面矩阵的路径有序乘积。该构造自然产生由端点投影和界面重叠组成的几何相位链，这些链在瞬时物质本征态的任意局域重相位下保持不变，从而解决了通常与开放路径输运相关的规范依赖歧义。所提出的形式体系阐明了分层介质中味演化的非对易性质，表明具有相同柱密度但不同排序的分布可产生不同的跃迁振幅。此外，我们分析了Dirac CP相位的影响，表明它会变形物质本征基输运的几何结构，但不等同于几何相位本身。在连续极限下，有限界面重叠收敛为Berry联络因子，而端点投影对于确保开放路径的规范不变性仍是不可或缺的。我们讨论了该结构的唯象学意义，强调几何相位并非独立可观测量，而是通过相干传播链之间的干涉对跃迁概率产生贡献。
英文摘要
We present a gauge invariant formulation of open path geometric phases in the context of three flavor neutrino oscillations traversing nonuniform matter. In contrast to the standard Berry phase, which is intrinsically associated with closed adiabatic cycles, neutrino propagation from source to detector typically traces an open trajectory within the parameter space of matter dependent Hamiltonians. We derive this formalism within a layered matter framework, where each discrete layer is characterized by a constant density and a local matter eigenbasis. The total evolution operator is expressed as a path ordered product of dynamical propagation factors and interface matrices that bridge adjacent matter eigenbases. This construction naturally yields geometric phase chains composed of endpoint projections and interface overlaps. We demonstrate that these chains remain invariant under arbitrary local rephasings of the instantaneous matter eigenstates, thereby resolving the gauge dependence ambiguity typically associated with open path transport. The proposed formalism elucidates the noncommutative nature of flavor evolution in layered media, illustrating that profiles with identical column densities but distinct ordering can yield different transition amplitudes. Furthermore, we analyze the influence of the Dirac CP phase, showing that it deforms the geometry of matter eigenbasis transport without being equivalent to the geometric phase itself. In the continuous limit, finite interface overlaps converge to Berry connection factors, while endpoint projections remain indispensable for ensuring open path gauge invariance. We discuss the phenomenological implications of this structure, emphasizing that geometric phases are not independent observables but contribute to transition probabilities via interference among coherent propagation chains.
