Riemann surface and quantization

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• 作者：E.E. Perepelkin^a ; ^{pevgeny@jinr.ru} ; B.I. Sadovnikov^a ; ^{sadovnikov@phys.msu.ru} ; N.G. Inozemtseva^b ; ^{nginozv@mail.ru}
• 关键词：Bohr&ndash ; Sommerfeld rule of quantization ; Feynman&rsquo ; s path integral ; Riemann surface ; The pilot wave theory ; Magnetic charge ; Dirac string
• 刊名：Annals of Physics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：376
• 期：Complete
• 页码：194-217
• 全文大小：1255 K
• 卷排序：376

文摘

This paper proposes an approach of the unified consideration of classical and quantum mechanics from the standpoint of the complex analysis effects. It turns out that quantization can be interpreted in terms of the Riemann surface corresponding to the multivalent LnΨLnΨ function. A visual interpretation of “trajectories” of the quantum system and of the Feynman’s path integral is presented. A magnetic dipole having a magnetic charge that satisfies the Dirac quantization rule was obtained.