A Compact Formula for Rotations as Spin Matrix Polynomials
Abstract
Group elements of SU(2) are expressed in closed form as finite polynomials of the Lie algebra generators, for all definite spin representations of the rotation group. The simple explicit result exhibits connections between group theory, combinatorics, and Fourier analysis, especially in the large spin limit. Salient intuitive features of the formula are illustrated and discussed.
 Publication:

SIGMA
 Pub Date:
 August 2014
 DOI:
 10.3842/SIGMA.2014.084
 arXiv:
 arXiv:1402.3541
 Bibcode:
 2014SIGMA..10..084C
 Keywords:

 spin matrices; matrix exponentials;
 Mathematical Physics;
 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 SIGMA 10 (2014), 084, 15 pages