相对论量子体系的相空间规范变换

Gauge transformation of phase space for quantized relativistic systems

汪克林等提出了量子体系的相空间规范变换(物理,2021,50(3):177).本文将此推广到相对论量子体系。相对论量子力学体现所需要的保能量的变换,是量子体系的变换r→r/α,p→pα再加上光速常数的变换c→c/α.以相对论的氢原子模型和谐振子模型为例进行了讨论。说明了普朗克常数是不做变换的。这样的规范变换适用于粒子做低动量运动的情况,因为时间未做变换,而在粒子运动时,根据洛伦兹变换,时间是会参与空间变换的。由此加深了我们对于量子力学体系相空间规范变换的认识。

Wang Ke-Lin et al.proposed a gauge transformation of phase space for quantized systems(Physics,2021,50(3):177).In the present paper,this gauge transformation is generalized to relativistic systems.In order to maintain the energy of a relativistic system invariant,the gauge transformation of phase space r→r/α,p→pαshould add a transformation of light speed constant c→c/α.This gauge transformation is applied to two examples:hydrogen model and harmonic oscillator model.It is explained that Planck constant remain unchanged.This kind of transformation is applicable to the cases where particles do low momentum motion.This is because time is untransformed,while according to Lorentz transformation,when a particle is moving,time will participate in space transformation.The present work deepens our understanding to the gauge transformation of phase space for quantized systems.