# A Compact Formula for Rotations as Spin Matrix Polynomials

@article{Curtright2014ACF, title={A Compact Formula for Rotations as Spin Matrix Polynomials}, author={Thomas L. Curtright and David B. Fairlie and C. Zachos}, journal={Symmetry, Integrability and Geometry: Methods and Applications}, year={2014} }

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.

## 16 Citations

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Recent results for rotations expressed as polynomials of spin matrices are derived here by elementary differential equation methods. Structural features of the results are then examined in the…

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