More on Rotations as Spin Matrix Polynomials
Abstract
Any nonsingular function of spin j matrices always reduces to a matrix polynomial of order 2j. The challenge is to find a convenient form for the coefficients of the matrix polynomial. The theory of biorthogonal systems is a useful framework to meet this challenge. Central factorial numbers play a key role in the theoretical development. Explicit polynomial coefficients for rotations expressed either as exponentials or as rational Cayley transforms are considered here. Structural features of the results are discussed and compared, and large j limits of the coefficients are examined.
Cite
@article{arxiv.1506.04648,
title = {More on Rotations as Spin Matrix Polynomials},
author = {Thomas L. Curtright},
journal= {arXiv preprint arXiv:1506.04648},
year = {2015}
}
Comments
Additional references, simplified derivation of Cayley transform polynomial coefficients, resolvent and exponential related by Laplace transform. Other minor changes to conform to published version to appear in J Math Phys