Riemann surface and quantization

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 LnΨ function. A visual interpretatio...

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Bibliographic Details
Published inAnnals of physics Vol. 376; pp. 194 - 217
Main Authors Perepelkin, E.E., Sadovnikov, B.I., Inozemtseva, N.G.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.01.2017
Subjects
Bohr–Sommerfeld rule of quantization
Dirac string
Feynman’s path integral
Magnetic charge
Riemann surface
The pilot wave theory
Feynman’s path integral
Dirac string
Bohr–Sommerfeld rule of quantization
Magnetic charge
The pilot wave theory
Riemann surface
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Summary: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 LnΨ 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.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2016.11.012