An Auxiliary 'Differential Measure' for $SU(3)$

TL;DR

This paper introduces an auxiliary differential measure for the $SU(3)$ group, enabling a calculus similar to $SU(2)$, and applies it to compute basis inner products and Clebsch-Gordan coefficients.

Contribution

The paper develops a differential measure approach for $SU(3)$, extending techniques analogous to $SU(2)$, and provides algebraic formulas for key group-theoretic quantities.

Findings

Derived an $SU(3)$ differential measure analogous to Schwinger's $SU(2)$ calculus.

Computed inner products of basis states using the new measure.

Obtained algebraic formulas for $SU(3)$ Clebsch-Gordan coefficients.

Abstract

A 'differential measure' is used to cast our calculus for the group $SU(3)$ into a form similar to Schwinger's boson operator calculus for the group $SU(2)$. It is then applied to compute (i) the inner product between the basis states and (ii) an algebraic formula for the Clebsch-Gordan coefficients. These were obtained earlier by us using Gaussian integration techniques.