非对易相空间及其狄拉克粒子在电磁场中的运动

Noncommutative phase space and the motion of Dirac particle in electromagnetic field

近年来,有关非对易空间的各种物理问题成为诸多学者研究的热点,并在量子力学、量子场论、量子电动力学、凝聚态物理、天体物理等各领域中被广泛探讨.本文通过非对易空间里电磁场中狄拉克粒子的哈密顿量,推导出速度算符和所受到的力算符的表达式,利用Bopp变换方法给出了电磁场作用下的狄拉克粒子在非对易空间和非对易相空间中的哈密顿量,从而推导出了速度算符和力算符的表达式,其中均包含因非对易引起的修正项.在此基础上进一步分析得出,非对易效应对狄拉克粒子的速度算符和所受到的力算符有一定的影响,但动量-动量算符的非对易性对粒子的速度算符没有影响.

In the past a few years, noncommutative space related problems are became a hot topic among a lot of researchers, and noncommutative space problems are extensively discussed in many field like quantum mechanics, quantum field theory, quantum electrodynamics, condense matter physics, astrophysics etc. In this article, we derive velocity operator and corresponding force operator thorough Hamiltonian of Dirac particle with electromagnetic field in the noncommutative space. By using the Bopp transformation, we provide Hamiltonian of Dirac particles with electromagnetic interaction in the noncommutative space and the noncommutative phase space, respectively. We also derive the expressions of velocity operator and force operator, which include correction term caused by noncommutativity. On these basis, we perform further analysis and have know that noncommutative effect has some influences to the velocity and force operators of the Dirac particle, but the noncommutative character of momentum-momentum operator has no influence to the velocity operator of Dirac particle.