On polynomials in spectral projections of spin operators
Mathematical Physics
2025-10-02 v2 math.MP
Representation Theory
Symplectic Geometry
Abstract
We show that the operator norm of an arbitrary bivariate polynomial, evaluated on certain spectral projections of spin operators, converges to the maximal value in the semiclassical limit. We contrast this limiting behavior with that of the polynomial when evaluated on random pairs of projections. The discrepancy is a consequence of a type of Slepian spectral concentration phenomenon, which we prove in some cases.
Keywords
Cite
@article{arxiv.2102.02613,
title = {On polynomials in spectral projections of spin operators},
author = {Ood Shabtai},
journal= {arXiv preprint arXiv:2102.02613},
year = {2025}
}
Comments
40 pages, 8 figures. Added result on a type of Slepian spectral concentration