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Weighted spherical monogenics

Abstract:

It is well known in Clifford analysis that monogenic functions are solutions of the Dirac operator and from a physical point of view, they are interpreted as functions that solve the relativistic equation of the motion of particles of spin 1/2, electrons, i.e that solve the physic Dirac equation. Functions with values in Clifford algebras can solve the weighted Dirac operator and these functions can belong to the internal space of functions that solve the Dirac equation for an anisotropic medium, where the weights do the effect of the different physical properties depending on the direction of motion in the medium. In this work, we extend the definition of spherical monogenics giving the definition of weighted spherical monogenics and found a basis for such polynomials.