2014/09/12 by Klaus Heinemann, James A. Ellison, Heinemann, Klaus +6
Computer Science · Decision Sciences · Mathematics · Physics and Astronomy · #Accelerator Physics (physics.acc-ph) #Cold Atom Physics and Bose-Einstein Condensates #Computational Physics and Python Applications #Distributed and Parallel Computing Systems #FOS: Physical sciences #Mathematical Physics (math-ph) #Scientific Computing and Data Management #math-ph #math.MP #physics.acc-ph
paper · pdf · doi:10.48550/arxiv.1409.4373
openalex publication_date 2014/09/12 · arxiv created 2014/12/12 · arxiv updated 2014/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
With this paper we extend our studies [1] on polarized beams by distilling tools from the theory of principal bundles. Four major theorems are presented, one which ties invariant fields with the notion of normal form, one which allows one to compare different invariant fields, and two that relate the existence of invariant fields to the existence of certain invariant sets and relations between them. We then apply the theory to the dynamics of spin-1/2 and spin-1 particles and their density matrices describing statistically the particle-spin content of bunches. Our approach thus unifies the spin-vector dynamics from the T-BMT equation with the spin-tensor dynamics and other dynamics. This unifying aspect of our approach relates the examples elegantly and uncovers relations between the various underlying dynamical systems in a transparent way.