The Gelfand-Tsetlin bases for spherical monogenics in dimension 3

Abstract

The main aim of this paper is to recall the notion of the Gelfand-Tsetlin bases (GT bases for short) and to use it for an explicit construction of orthogonal bases for the spaces of spherical monogenics (i.e., homogeneous solutions of the Dirac or the generalized Cauchy-Riemann equation, respectively) in dimension 3. In the paper, using the GT construction, we obtain explicit orthogonal bases for spherical monogenics in dimension 3 having the Appell property and we compare them with those constructed by the first and the second author recently (by a direct analytic approach).