标题： 具有流形积空间上通量的狄拉克方程的可积性 显示英文标题

标题： Integrability of the Dirac Equation in the Presence of Fluxes on Product Manifolds

摘要： 本文旨在证明与任意非均匀通量场耦合的狄拉克方程在由双维空间的直积形成的流形上允许分离变量。 作为这些结果的直接应用，我们研究了一个自旋为$1/2$的带电粒子在背景场中传播，该背景场与一种新颖且复杂的弦启发模型在$D = 10$维时空下共形相关，其底流形是四个二维单位球$S^{2}$的乘积，并且存在$1$-形式和$3$-形式的通量场。 显示英文摘要

摘要： This paper aims to show that the Dirac equation coupled to an arbitrary inhomogeneous flux field admits separation in manifolds formed from the direct product of bidimensional spaces. As a direct application of these results, we study a spin-$1/2$ charged particle propagating in a background conformally related to a novel and complex string-inspired model in $D = 10$ spacetime dimension whose base manifold is a product of four two-dimensional unit spheres, $S^{2}$, in the presence of $1$- and $3$-form fluxes.