Thomas L. Curtright, David B. Fairlie, Cosmas K. Zachos, “A Compact Formula for Rotations as Spin Matrix Polynomials”, SIGMA, 2014, Volume 10,084, 15 pp.

This article is cited in 18 papers

A Compact Formula for Rotations as Spin Matrix Polynomials

Thomas L. Curtright^a, David B. Fairlie^b, Cosmas K. Zachos^c

^a Department of Physics, University of Miami, Coral Gables, FL 33124-8046, USA
^b Department of Mathematical Sciences, Durham University, Durham, DH1 3LE, UK
^c High Energy Physics Division, Argonne National Laboratory, Argonne, IL 60439-4815, USA

Abstract: Group elements of $\mathrm{SU}(2)$ 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.

Keywords: spin matrices; matrix exponentials.

MSC: 15A16; 15A30

Received: May 7, 2014; in final form August 7, 2014; Published online August 12, 2014

Language: English

DOI: 10.3842/SIGMA.2014.084