论文标题
来自拓扑电磁的Finsler几何形状
Finsler Geometries from Topological Electromagnetism
论文作者
论文摘要
我们分析了外部拉尼达场中无旋转和旋转电动颗粒的运动学空间的鳍片几何形状。我们考虑在洛伦兹，电磁仪和重新训练转换下不变的最通用的动作。在每种情况下，Finsler几何形式形成由量规场参数的集合。我们提供了一种简单的方法来计算粒子在通用电磁场中粒子运动学空间的鳍片几何形状的基本对象。然后，我们应用这种方法来计算无旋转和旋转颗粒的测量方程。另外，我们表明Rañada背景中的电磁二元性在一组Finsler几何形状中引起了简单的双图。二元图图具有与电磁电位相互作用的电动粒子和与双重电磁电位相互作用的磁性电粒子的简单解释。我们通过计算双重测量方程来体现偶性图的作用。
We analyse the Finsler geometries of the kinematic space of spinless and spinning electrically charged particles in an external Rañada field. We consider the most general actions that are invariant under the Lorentz, electromagnetic gauge and reparametrization transformations. The Finsler geometries form a set parametrized by the gauge fields in each case. We give a simple method to calculate the fundamental objects of the Finsler geometry of the kinematic space of a particle in a generic electromagnetic field. Then we apply this method to calculate the geodesic equations of the spinless and spinning particles. Also, we show that the electromagnetic duality in the Rañada background induces a simple dual map in the set of Finsler geometries. The duality map has a simple interpretation in terms of an electrically charged particle that interacts with the electromagnetic potential and a magnetically charged particle that interacts with the dual magnetoelectric potential. We exemplify the action of the duality map by calculating the dual geodesic equation.
