A compact formula for rotations as spin matrix polynomials

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

Research output: Contribution to journalArticle

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 languageEnglish (US)
Article number084
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume10
DOIs
StatePublished - 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

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 journalArticle

@article{af9da49e6ed04cc889b336ec278a414b,
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 = "Thomas Curtright and Fairlie, {David B.} and Zachos, {Cosmas K.}",
year = "2014",
month = "8",
day = "12",
doi = "10.3842/SIGMA.2014.084",
language = "English (US)",
volume = "10",
journal = "Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)",
issn = "1815-0659",
publisher = "Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine",

}

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 -