Elementary results for the fundamental representation of SU(3)
Thomas L. Curtright, Cosmas K. Zachos
TL;DR
This paper derives a general expression for SU(3) fundamental representation elements as a polynomial in the generator matrix, involving elementary functions and the determinant invariant.
Contribution
It provides a novel polynomial formulation of SU(3) elements in the fundamental representation based on the generator matrix and its determinant.
Findings
Expresses SU(3) elements as second order polynomials in H
Uses elementary trigonometric functions dependent on det(H)
Offers a new analytical tool for SU(3) representation analysis
Abstract
A general group element for the fundamental representation of SU(3) is expressed as a second order polynomial in the hermitian generating matrix H, with coefficients consisting of elementary trigonometric functions dependent on the sole invariant det(H), in addition to the group parameter.
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