A compact formula for rotations as spin matrix polynomials

Thomas Curtright; David B. Fairlie; Cosmas K. Zachos

doi:10.3842/SIGMA.2014.084

A compact formula for rotations as spin matrix polynomials

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

Physics

Research output: Contribution to journal › Article

9 Citations (Scopus)

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	https://doi.org/10.3842/SIGMA.2014.084
State	Published - Aug 12 2014

Fingerprint

Matrix Polynomial

Rotation Group

Fourier Analysis

Group Theory

Combinatorics

Intuitive

Lie Algebra

Closed-form

Generator

Polynomial

Keywords

Matrix exponentials
Spin matrices

ASJC Scopus subject areas

Analysis
Geometry and Topology
Mathematical Physics

Cite this

Curtright, T., Fairlie, D. B., & Zachos, C. K. (2014). A compact formula for rotations as spin matrix polynomials. 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.

In: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), Vol. 10, 084, 12.08.2014.

Research output: Contribution to journal › Article

Curtright, T, Fairlie, DB & Zachos, CK 2014, 'A compact formula for rotations as spin matrix polynomials', Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), vol. 10, 084. https://doi.org/10.3842/SIGMA.2014.084

Curtright T, Fairlie DB, Zachos CK. A compact formula for rotations as spin matrix polynomials. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2014 Aug 12;10. 084. https://doi.org/10.3842/SIGMA.2014.084

Curtright, Thomas ; Fairlie, David B. ; Zachos, Cosmas K. / A compact formula for rotations as spin matrix polynomials. In: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2014 ; Vol. 10.

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Access to Document

10.3842/SIGMA.2014.084