A Set of Harmonic Functions for the Group SU(3) as Specialized Matrix Elements of a General Finite Transformation

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Abstract
A straightforward method of converting the commutation rules of the generators of a group into a set of differential equations is developed. The detailed development is applied to SU(3). Differential operators having the correct commutators are constructed and then combined into the quadratic and cubic combinations of the two Casimir operators. The solution of the resulting set of differential equations is the matrix element of a general finite transformation with the right‐hand state specialized to the isotopic spin singlet. The set of such matrix elements is equivalent to the set of SU(3) harmonic functions derived by Beg and Ruegg. The isotopic spin‐hypercharge content of the irreducible representations of SU(3) is deduced from the form of the matrix element, though prior knowledge of the fact that each irreducible representation of SU(3) possesses an isotopic spin singlet is assumed.

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