A Compact Formula for Rotations as Spin Matrix Polynomials

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

doi:10.3842/SIGMA.2014.084

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. Here, 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.

Authors:

Curtright, Thomas L. ^[1]; Fairlie, David B. ^[2]; Zachos, Cosmas K. ^[3]

Univ. of Miami, Coral Gables, FL (United States)
Durham Univ., Durham (United Kingdom)
Argonne National Lab. (ANL), Argonne, IL (United States)

Publication Date:: Tue Aug 12 00:00:00 EDT 2014

Research Org.:: Argonne National Lab. (ANL), Argonne, IL (United States)

Sponsoring Org.:: Argonne National Laboratory; USDOE Office of Science (SC)

OSTI Identifier:: 1395147

Grant/Contract Number:: AC02-06CH11357

Resource Type:: Accepted Manuscript

Journal Name:: Symmetry, Integrability and Geometry: Methods and Applications

Additional Journal Information:: Journal Volume: 10; Journal ID: ISSN 1815-0659

Publisher:: Institute of Mathematics, National Academy of Sciences Ukraine

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; spin matrices; matrix exponentials

Citation Formats


                    Curtright, Thomas L., Fairlie, David B., and Zachos, Cosmas K. A Compact Formula for Rotations as Spin Matrix Polynomials.  United States: N. p., 2014. 
Web.  doi:10.3842/SIGMA.2014.084.

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                    Curtright, Thomas L., Fairlie, David B., & Zachos, Cosmas K. A Compact Formula for Rotations as Spin Matrix Polynomials.  United States.  https://doi.org/10.3842/SIGMA.2014.084

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                    Curtright, Thomas L., Fairlie, David B., and Zachos, Cosmas K. Tue .  
"A Compact Formula for Rotations as Spin Matrix Polynomials".  United States.  https://doi.org/10.3842/SIGMA.2014.084.  https://www.osti.gov/servlets/purl/1395147.

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@article{osti_1395147,

  title        = {A Compact Formula for Rotations as Spin Matrix Polynomials},

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

  abstractNote = {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. Here, 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.},

  doi          = {10.3842/SIGMA.2014.084},

  journal      = {Symmetry, Integrability and Geometry: Methods and Applications},

  number       = ,

  volume       = 10,

  place        = {United States},

  year         = {Tue Aug 12 00:00:00 EDT 2014},

  month        = {Tue Aug 12 00:00:00 EDT 2014}

}

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Topology and entanglement in quench dynamics
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Physical Review B, Vol. 97, Issue 22
DOI: 10.1103/physrevb.97.224304

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Title: A Compact Formula for Rotations as Spin Matrix Polynomials

Abstract

Citation Formats

Topology and entanglement in quench dynamics journal, June 2018

Topology and entanglement in quench dynamics
journal, June 2018