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Communications in Theoretical Physics

Gauge Transformation and Constraint Induced Operator Ordering for Charged Rigid Planar Rotator in Uniform Magnetic Field

Lai Mei-Mei, Wang Xin, Yanping Xiao, Quanhui Liu

Published Nov 1, 2006• 1 citation
Publisher

Abstract

When the motion of a particle is constrained, excess terms exist using hermitian form of Cartesian momentum p i ( i = 1,2,3) in usual kinetic energy (1/2μ)∑ p i 2 , and the correct kinetic energy turns out to be (1/2μ)∑1/ f i p i f i p i , where f i are dummy factors in classical mechanics and nontrivial in quantum mechanics. In this paper the explicit form of the dummy functions f i is given for a charged rigid planar rotator in the uniform magnetic field with different gauge chosen. Under different gauges, we have different sets of dummy factors. It means that these factors do not have direct observable effect.

DOI
10.1088/0253-6102/46/5/014

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When the motion of a particle is constrained, excess terms exist using hermitian form of Cartesian momentum p i ( i = 1,2,3) in usual kinetic energy (1/2μ)∑ p i 2 , and the correct kinetic energy turns out to be (1/2μ)∑1/ f i p i f i p i , where f i are dummy factors in classical mechanics and nontrivial in quantum mechanics. In this paper the explicit form of the dummy functions f i is given for a charged rigid planar rotator in the uniform magnetic field with different gauge chosen. Under different gauges, we have different sets of dummy factors. It means that these factors do not have direct observable effect.
当一个粒子的运动被抑制时，过量条款存在笛卡儿的动量 p_i 的 usinghermitian 形式( i = 1,2 ， 3 )在平常的动能( 1/2 μ) ∑p _i~2 ，和正确动能结果是( 1/2 μ) ∑1 /f_iP_if_iP_i ，在 f_i 是在古典力学的哑巴因素的地方并且在量力学重要。在这篇论文，哑巴功能 f_i 的明确的表格在一致磁场为一个控告的僵硬平面转子被给，不同计量器选择。在不同计量器下面，我们有哑巴因素的不同集合。它意味着这些因素没有直接可见的效果。