论文标题
带电颗粒在带有球形和双曲对称磁场的空间中运动的运动
Motion of charged particles in spacetimes with magnetic fields of spherical and hyperbolic symmetry
论文作者
论文摘要
考虑到具有恒定正曲率或负曲率的亚体的带电颗粒的运动，电磁张张量与亚体的体积的两种形式成正比。在正弯曲情况下，这描述了带有磁单极的球形对称空间，而在负曲率情况下，它是双曲线时空，沿双曲线表面磁场均匀。通过考虑在具有量规旋转力量的相空间上定义的泊松支架，可以找到运动的常数。在球形对称的情况下，我们在圆锥形缺陷时段中与赤道测量学的庞加莱锥上的轨迹之间的对应关系。在双曲线的情况下，庞加莱锥的类似物被定义为辅助Minkowski时空中的表面。为Minkowski，$ \ mathrm {ads} _4 \ times s^2 $和双曲线ADS-REISSNER-NORDSTRömSpaceTimes解决了明确的示例。
The motion of charged particles in spacetimes containing a submanifold of constant positive or negative curvature is considered, with the electromagnetic tensor proportional to the volume two-form form of the submanifold. In the positive curvature case, this describes spherically symmetric spacetimes with a magnetic monopole, while in the negative curvature case, it is a hyperbolic spacetime with magnetic field uniform along hyperbolic surfaces. Constants of motion are found by considering Poisson brackets defined on a phase space with gauge-covariant momenta. In the spherically-symmetric case, we find a correspondence between the trajectories on the Poincaré cone with equatorial geodesics in a conical defect spacetime. In the hyperbolic case, the analogue of the Poincaré cone is defined as a surface in an auxiliary Minkowski spacetime. Explicit examples are solved for the Minkowski, $\mathrm{AdS}_4\times S^2$, and the hyperbolic AdS-Reissner--Nordström spacetimes.
