A compact formula for rotations as spin matrix polynomials

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

doi:10.3842/SIGMA.2014.084

A compact formula for rotations as spin matrix polynomials

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

Physics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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

Keywords

Matrix exponentials
Spin matrices

ASJC Scopus subject areas

Analysis
Mathematical Physics
Geometry and Topology

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10.3842/SIGMA.2014.084

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title = "A compact formula for rotations as spin matrix polynomials",

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.",

keywords = "Matrix exponentials, Spin matrices",

author = "Curtright, {Thomas L.} and Fairlie, {David B.} and Zachos, {Cosmas K.}",

year = "2014",

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AU - Curtright, Thomas L.

AU - Fairlie, David B.

AU - Zachos, Cosmas K.

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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

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M3 - Article

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ER -

A compact formula for rotations as spin matrix polynomials

Abstract

Keywords

ASJC Scopus subject areas

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