Comparison of Spin Dynamics in the Cylindrical and Frenet-Serret Coordinate Systems
Alexander J. Silenko
TL;DR
This paper compares spin dynamics descriptions in cylindrical and Frenet-Serret coordinate systems, demonstrating their equivalence and highlighting the practical advantages of the cylindrical system for accelerator physics applications.
Contribution
It establishes the equivalence of the two coordinate systems and advocates for the cylindrical system's efficiency in calculating spin evolution in accelerators.
Findings
Cylindrical and Frenet-Serret systems are equivalent for spin dynamics.
Cylindrical coordinates offer practical advantages for accelerator calculations.
The study enhances understanding of coordinate system choices in spin physics.
Abstract
A comparative analysis of a description of spin dynamics in the cylindrical and Frenet-Serret coordinate systems is carried out. An equivalence of these two systems is shown. A possibility of efficient use of the cylindrical coordinate system for a calculation of spin evolution of particles and nuclei in accelerators and storage rings is caused by an immobility of its coordinate axes relative to stationary detectors.
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