A rational theory for Clebsch-Gordan coefficients

TL;DR

This paper develops a rational-number-based theory for Clebsch-Gordan coefficients of SL(2,C), including orthogonality, recurrence, and symmetry properties, with an efficient computational algorithm.

Contribution

It introduces a novel rational framework for Clebsch-Gordan coefficients, simplifying calculations and revealing new symmetry and recurrence relations.

Findings

Rational number formulation of Clebsch-Gordan coefficients

Derivation of orthogonality and recurrence relations

Development of an efficient Pascal's recurrence-based algorithm

Abstract

A theory of Clebsch-Gordan coefficients for $SL(2, C)$ is given using only rational numbers. Features include orthogonality relations, recurrence relations, and Regge's symmetry group. Results follow from elementary representation theory and properties of binomial coefficients. A computational algorithm is given based on Pascal's recurrence.