An Algebraic Theory of Non-Relativistic Spin
Quantum Physics
2022-10-07 v2 Mathematical Physics
math.MP
Abstract
In this paper we present a new, elementary derivation of non-relativistic spin using exclusively real algebraic methods. To do this, we formulate a novel method to decompose the domain of a real endomorphism according to its algebraic properties. We reveal non-commutative multipole tensors as the primary physically meaningful observables of spin, and indicate that spin is fundamentally geometric in nature. In so doing, we demonstrate that neither dynamics nor complex numbers are essential to the fundamental description of spin.
Keywords
Cite
@article{arxiv.2207.02351,
title = {An Algebraic Theory of Non-Relativistic Spin},
author = {Peter T. J. Bradshaw},
journal= {arXiv preprint arXiv:2207.02351},
year = {2022}
}
Comments
27 pages, 1 figure, 2 tables, v2 changes: Restructured introduction. Restructured arguments to use the step maps earlier. Added step-level and step-up in terms of multipoles. Fixed typos