We give an informal summary of ongoing work which uses tools distilled from
the theory of fibre bundles to classify and connect invariant fields associated
with spin motion in storage rings. We mention four major theorems. One ties
invariant fields with the notion of normal form, the second allows comparison
of different invariant fields and the two others tie the existence of invariant
fields to the existence of certain invariant sets. We explain how the theorems
apply to the spin dynamics of spin-1/2 and spin-1 particles. Our approach
elegantly unifies the spin-vector dynamics from the T-BMT equation with the
spin-tensor dynamics and other dynamics and suggests an avenue for addressing
the question of the existence of the invariant spin field.Comment: Based on a presentation at Spin2014, The 21st International Symposium
on Spin Physics, Beijing, China, October 2014. To be published in the
International Journal of Modern Physics, Conference Serie
