Symplectic areas, quantization, and dynamics in electromagnetic fields
Symplectic areas, quantization, and dynamics in electromagnetic fields
复制标题
电磁场中的辛区域、量子化和动力学
DOI：
10.1063/1.1426688
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发表时间：
2000
影响因子：
1.3
通讯作者：
T. A. Osborn
中科院分区：
文献类型：
--
作者：
M. Karasev;T. A. Osborn
在具有非均匀法拉第电磁张量的线性相空间中，发展了封闭积分形式的规范不变量子化。通过一个膜磁区得到了Groenewold乘积公式（对应于Weyl序）的一个类似形式，并推广到N个符号的乘积.量子化中的排序问题与膜的不同配置有关：配置的选择决定了固定排序的相位因子，并控制次级相空间上的辛群胚结构。本文给出了电磁场中带电粒子量子演化问题的规范不变解的精确连续形式和通过动力膜面积的半经典近似。
A gauge invariant quantization in a closed integral form is developed over a linear phase space endowed with an inhomogeneous Faraday electromagnetic tensor. An analog of the Groenewold product formula (corresponding to Weyl ordering) is obtained via a membrane magnetic area, and extended to the product of N symbols. The problem of ordering in quantization is related to different configurations of membranes: A choice of configuration determines a phase factor that fixes the ordering and controls a symplectic groupoid structure on the secondary phase space. A gauge invariant solution of the quantum evolution problem for a charged particle in an electromagnetic field is represented in an exact continual form and in the semiclassical approximation via the area of dynamical membranes.