A CALCULUS FOR SU(3) LEADING TO AN ALGEBRAIC FORMULA FOR THE CLEBSCH-GORDAN-COEFFICIENTS

We develop a simple computational tool for SU(3) analogous to Bargmann 's calculus for SU(2). Crucial new inputs are (i) explicit representat ion of the Gelfand-Zetlin basis in terms of polynomials in four variab les and positive or negative integral powers of a fifth variable, (ii) an auxiliary Gaussian measure with respect to which the Gelfand-Zetli n states an orthogonal but not normalized, (iii) simple generating fun ctions for generating all basis states and also all invariants, As an illustration of our techniques, an algebraic formula for the Clebsch-G ordan coefficients is obtained for the first time. This involves only Gaussian integrations. Thus SU(3) is made as accessible for computatio ns as SU(2) is. (C) 1996 American Institute of Physics.