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    • The algebra and geometry ofSU(3) matrices

      K S Mallesh N Mukunda

      Research Articles Volume 49 Issue 4 October 1997 pp 371-383

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pram/049/04/0371-0383

    • Keywords

       

      SU(3) matrices; octet algebra; octet geometry; SU(3) axis-angle parameters

    • Abstract

       

      We give an elementary treatment of the defining representation and Lie algebra of the three-dimensional unitary unimodular groupSU(3). The geometrical properties of the Lie algebra, which is an eight dimensional real linear vector space, are developed in anSU(3) covariant manner. Thef andd symbols ofSU(3) lead to two ways of ‘multiplying’ two vectors to produce a third, and several useful geometric and algebraic identities are derived. The axis-angle parametrization ofSU(3) is developed as a generalization of that forSU(2), and the specifically new features are brought out. Application to the dynamics of three-level systems is outlined.

    • Author Affiliations

       

      K S Mallesh1 N Mukunda1 2 3

      1. Department of Studies in Physics, University of Mysore, Mysore - 570 006, India
      2. Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore - 560 064, India
      3. Centre for Theoretical Studies and Department of Physics, Indian Institute of Science, Bangalore - 560 012, India

    • Dates

       
      Published
      October 1997
      Manuscript received
      13 March 1997

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