A compact formula for rotations as spin matrix polynomials

Thomas L. Curtright, David B. Fairlie, Cosmas K. Zachos

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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.

Original languageEnglish (US)
Article number084
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
StatePublished - Aug 12 2014


  • Matrix exponentials
  • Spin matrices

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Geometry and Topology


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