关于量子理论中的广义规范无关性问题

On Generalized Gauge Independence in Quantum Theory

可以用无穷多个彼此规范等价的Ｈａｍｉｌｔｏｎｉａｎ来描写同一个具有经典对应的量子动力学系统，即存在Ｈａｍｉｌｔｏｎｉａｎ选取的广义规范任意性。作者在代数动力学框架内讨论这类广义规范性问题，给出了一种构造量子动力学方程广义规范协变解的方法。以广义含时谐振子为例，构造了新的量子不变量，它的行为取决于相应经典运动方程的解；证明了量子态在演化过程中所获得的位相是广义规范无关的。

It is possible to use an infinite Hamiltonians,which are gauge equivalent to each other,to describe a common dynamic system,that is, selection of a Hamiltonian is arbitrary.A method to construct a gauge covariant solution to quantum dynamic equations in the frame work of algebraic dynamics is proposed.As an example,a dynamic invariant is constructed for the generalized time dependent harmonic oscillator by employing the solution to the corresponding classical equations of motion.It is shown that the Lewis Riesenfeld phase is manifestly gauge independent.