On a charged spinless point particle minimally coupled to a constant magnetic field in a noncommutative plane
arXiv:2211.07192 · doi:10.1016/j.aop.2023.169308
Abstract
In this paper, we provide a mathematically and physically consistent minimal prescription for a charged spinless point particle coupled to a constant magnetic field in a 2-dimensional noncommutative plane. It turns out to be a gauge invariant prescription in contrast to the widely and carelessly used naive minimal prescription in the context of 2-dimensional quantum mechanics in a noncommutative plane. Besides, we explore the noncommutative U(1) gauge theoretic structure of the underlying noncommutative system by explicitly computing the 1-parameter family of Seiberg-Witten maps.
arXiv comment20 pages, typos corrected, references updated, Introduction expanded, Appendix containing derivation of gauge function added, accepted version to appear in Annals of Physics
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