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The algebra and geometry of SU(3) matrices

Mallesh, KS and Mukunda, N (1997) The algebra and geometry of SU(3) matrices. In: Pramana - Journal of Physics, 49 (4). pp. 371-383.

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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: Journal Article
Publication: Pramana - Journal of Physics
Publisher: Indian Academy of Sciences
Additional Information: Copyright of this article belongs to Indian Academy of Sciences.
Keywords: SU(3) matrices;octet algebra;octet geometry;SU(3) axis-angle parameters.
Department/Centre: Division of Physical & Mathematical Sciences > Centre for Theoretical Studies (Ceased to exist at the end of 2003)
Division of Physical & Mathematical Sciences > Physics
Date Deposited: 22 Jun 2011 07:29
Last Modified: 22 Jun 2011 07:29
URI: http://eprints.iisc.ac.in/id/eprint/38532

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