The Clobsch-Gordan Coefficients

Su(3) Clebsch-gordan Coefficients

The purpose of this paper is to find out a set of general recurrence formulas for the calculus of the SU(3) Clebsch-Gordan coefficients. The first six sections are introductory, presenting the notations and general group theoretical methods applied to SU(3). The following eight sections are devoted to a detailed treatment of the carrier spaces of the irreducible representations and their direct...

2 00 1 Clebsch - Gordan coefficients and the binomial distribution

There appear to be two standard ways of calculation C-G coefficients in quantum mechanics. One method is to combine the “ladder” operator approach with orthogonality conditions. The second method is to use some type of closed form [2] which allows the coefficients to be calculated directly. However, the latter approach is at times considered “tedious” [2] and does not reveal any new information...

On the Computation of Clebsch-Gordan Coefficients and the Dilation Effect

On the Computation of Clebsch – Gordan Coefficients and the Dilation effect ∗ Jesús

We investigate the problem of computing tensor product multiplicities for complex semisimple Lie algebras. Even though computing these numbers is #P -hard in general, we show that if the rank of the Lie algebra is assumed fixed, then there is a polynomial time algorithm, based on counting the lattice points in polytopes. In fact, for Lie algebras of type Ar, there is an algorithm, based on the ...

Invariants of Colored Links and a Property of the Clebsch-gordan Coefficients of U Q (g)

Abstract. We show that multivariable colored link invariants are derived from the roots of unity representations of Uq(g). We propose a property of the Clebsch-Gordan coefficients of Uq(g), which is important for defining the invariants of colored links. For Uq(sl2) we explicitly prove the property, and then construct invariants of colored links and colored ribbon graphs, which generalize the m...