二维纯规范场和半量子涡旋中的库仑-量子振子对应
Coulomb- quantum oscillator correspondence in two dimension, pure gauge field and half-quantized vortex
摘要：
各向同性振子和库仑问题有着有趣的对应关系。我们专注于二维量子问题，并提出完整的治疗对应，包括薛定谔方程，本征函数和本征值，和运动的积分。我们发现只有部分等价。引入局域规范变换检查了波函数对应，并建立了具有相关自旋半的半量子化涡旋的出现。本文讨论了我们提出的电子的涡旋结构和电荷的来源。展望了量子色动力学和强子谱的意义。
英文摘要：
Isotropic oscillator and Coulomb problems are known to have interesting correspondence. We focus on 2D quantum problems and present complete treatment on the correspondence including the Schroedinger equation, eigenfunctions and eigenvalues, and the integrals of motion. We find only partial equivalence. The wavefunction correspondence is examined introducing local gauge transformation and the emergence of half-quantized vortex with the associated spin-half is established. Vortex structure of the electron proposed by us and the origin of charge are discussed in the present context. Outlook on the implications for QCD and hadron spectrum is outlined.
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