The Kronecker product in terms of Hubbard operators and the Clebsch–Gordan decomposition of image Original Research Article

We review the properties of the Kronecker (direct, or tensor) product of square matrices image in terms of Hubbard operators. In its simplest form, a Hubbard operator image can be expressed as the image-square matrix which has entry 1 in position image and zero in all other entries. The algebra and group properties of the observables that define a multipartite quantum system are notably straightforward in such a framework. In particular, we use the Kronecker product in Hubbard notation to get the Clebsch–Gordan decomposition of the product group image. Finally, the image-dimensional irreducible representations so obtained are used to derive closed forms of the Clebsch–Gordan coefficients that rule the addition of angular momenta. Our results can be further developed in many different directions.