有电流存在时受约束带电粒子的量子力学
Quantum mechanics of a constrained electrically charged particle in the presence of electric currents
摘要：
本文讨论了在普通三维空间中，带电荷的经典无自旋量子粒子在非奇异静态表面上运动的动力学，其中存在任意组态的与时间无关的电流.从嵌入空间中的正则作用出发，我们证明了带电荷的带电粒子$q$耦合到$qA^3M$中的一个线性项，其中$A^3$是电磁矢势的横向分量，$M$是表面的平均曲率。这一项正好抵消了曲率对粒子轨道磁矩的贡献。它示出的粒子，独立的值的电荷，除了已知的耦合的几何形状也耦合到平均曲率的表面时，诺依曼型的约束施加在横向波动的波函数。与对横向涨落的狄利克雷约束相反，对这些自由度的诺依曼型约束一般会使运动方程不可分。例外的是在具有恒定平均曲率的表面上的电中性粒子的运动方程。在存在电流的情况下，带电粒子的运动方程通常是不可分离的，与几何形状和边界约束的耦合无关。
英文摘要：
We discuss the dynamics of a classical spinless quantum particle carrying electric charge and constrained to move on a non singular static surface in ordinary three dimensional space in the presence of arbitrary configurations of time independent electric currents. Starting from the canonical action in the embedding space we show that a charged particle with charge $q$ couples to a term linear in $qA^3M$, where $A^3$ is the transverse component of the electromagnetic vector potential and $M$ is the mean curvature in the surface. This term cancels exactly a curvature contribution to the orbital magnetic moment of the particle. It is shown that particles, independently of the value of the charge, in addition to the known couplings to the geometry also couple to the mean curvature in the surface when a Neumann type of constraint is applied on the transverse fluctuations of the wave function. In contrast to a Dirrichlet constraint on the transverse fluctuations a Neumann type of constraint on these degrees of freedom will in general make the equations of motion non separable. The exceptions are the equations of motion for electrically neutral particles on surfaces with constant mean curvature. In the presence of electric currents the equation of motion of a charged particle is generally non separable independently of the coupling to the geometry and the boundary constraints.
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