The algebra and geometry of SU(3) matrices

Mallesh, K. S. ; Mukunda, N. (1997) The algebra and geometry of SU(3) matrices Pramana - Journal of Physics, 49 (4). pp. 371-383. ISSN 0304-4289

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We give an elementary treatment of the defining representation and Lie algebra of the three-dimensional unitary unimodular group SU(3). The geometrical properties of the Lie algebra, which is an eight dimensional real linear vector space, are developed in an SU(3) covariant manner. The f and d symbols of SU(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 of SU(3) is developed as a generalization of that for SU(2), and the specifically new features are brought out. Application to the dynamics of three-level systems is outlined.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:SU(3) Matrices; Octet Algebra; Octet Geometry; SU(3) Axis-angle Parameters
ID Code:78455
Deposited On:20 Jan 2012 04:12
Last Modified:18 May 2016 21:16

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