A Compact Formula for Rotations as Spin Matrix Polynomials

;
• Fairlie, David B.
;
• Zachos, Cosmas K.

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.