Assembling Cartesian Harmonic Tensors

Abstract

Cartesian harmonic tensors are completely symmetric traceless tensors in three dimensional space constructed from the direct product of unit vectors. They are useful in generating expressions for the angular coupling of spherical harmonics of differing solid angles in terms of scalar and vector products of the unit vectors for the spherical harmonics involved. A presentation for the algebraic programming of Cartesian harmonic tensors of arbitrary rank is given using Algebraic Assembly Language. Results are checked using Mathematica.