### 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.

Original language | English (US) |
---|---|

Article number | 084 |

Journal | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |

Volume | 10 |

DOIs | |

State | Published - Aug 12 2014 |

### Fingerprint

### Keywords

- Matrix exponentials
- Spin matrices

### ASJC Scopus subject areas

- Analysis
- Geometry and Topology
- Mathematical Physics

### Cite this

*Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)*,

*10*, [084]. https://doi.org/10.3842/SIGMA.2014.084

**A compact formula for rotations as spin matrix polynomials.** / Curtright, Thomas; Fairlie, David B.; Zachos, Cosmas K.

Research output: Contribution to journal › Article

*Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)*, vol. 10, 084. https://doi.org/10.3842/SIGMA.2014.084

}

TY - JOUR

T1 - A compact formula for rotations as spin matrix polynomials

AU - Curtright, Thomas

AU - Fairlie, David B.

AU - Zachos, Cosmas K.

PY - 2014/8/12

Y1 - 2014/8/12

N2 - 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.

AB - 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.

KW - Matrix exponentials

KW - Spin matrices

UR - http://www.scopus.com/inward/record.url?scp=84907347047&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84907347047&partnerID=8YFLogxK

U2 - 10.3842/SIGMA.2014.084

DO - 10.3842/SIGMA.2014.084

M3 - Article

AN - SCOPUS:84907347047

VL - 10

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SN - 1815-0659

M1 - 084

ER -