基于力学动量构造的平移算符与AB效应

AB effect and transport operator based on the mechanical momentum

当存在磁场时,动量算符分为力学动量和正则动量,其中力学动量对应于速度,但是量子力学不引入基于力学动量构造的平移算符.当讨论AB效应时,常常借助动力学方法.本文指出,电磁场作为一种规范场引入现代物理,其实相当于引入基于力学动量构造的平移算符,而让这一算符沿一个闭合回路绕行一周且回路中包含了非零磁通量,将直接给出AB效应.这种方法直接显示出AB效应的几何本质.

In the presence of a magnetic field,the momentum can be classified into mechanical and canonical one,where the mechanical momentum corresponds to the velocity,and quantum mechanics has seldem introduced the transport operator via the mechanical momentum.When the AB effect is discussed,the dynamical method is uaually invoked.Once the transport operator is formed and is taken round the trips circuiting the magnetic field,AB effect is reproduced.Our method explicitly exhibits the geometrical nature of the AB effect.