Advertisement

Pramana

, Volume 49, Issue 4, pp 371–383 | Cite as

The algebra and geometry ofSU(3) matrices

  • K S Mallesh
  • N Mukunda
Research Articles

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.

Keywords

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

PACS Nos

02.20 03.65 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    D Griffiths,Introduction to elementary particles (John Wiley and Sons, New York, 1983)Google Scholar
  2. [2]
    C Quigg,Gauge theories of the strong, weak and electromagnetic interactions (The Benjamin-Cummings Pub. Co., London, 1983)Google Scholar
  3. [3]
    J N Elgin,Phys. Lett. A80, 140 (1980)ADSGoogle Scholar
  4. [4]
    P K Aravind,J. Opt. Soc. Am. B3, 1025 (1986)ADSGoogle Scholar
  5. [5]
    F T Hioe,Phys. Rev. A28, 879 (1983)ADSMathSciNetGoogle Scholar
  6. [6]
    M Gell-Mann and Y Neeman,The eightfold way (W A Benjamin Inc., New York, 1964)Google Scholar
  7. [7]
    J J de Swart,Rev. Mod. Phys. 35, 916 (1963)CrossRefADSGoogle Scholar
  8. [8]
    G Khanna, S Mukhopadhyay, R Simon and N Mukunda,Ann. Phys. (NY) 253, 55 (1997)zbMATHCrossRefADSMathSciNetGoogle Scholar

Copyright information

© the Indian Academy of Sciences 1997

Authors and Affiliations

  • K S Mallesh
    • 1
  • N Mukunda
    • 1
    • 3
    • 2
  1. 1.Department of Studies in PhysicsUniversity of MysoreMysoreIndia
  2. 2.Centre for Theoretical Studies and Department of PhysicsIndian Institute of ScienceBangaloreIndia
  3. 3.Jawaharlal Nehru Centre for Advanced Scientific ResearchJakkur, BangaloreIndia

Personalised recommendations