Algebraic and differential equations for spinning particles on the sphere

We revise the mathematical formulation of the theory of a particle in a spherical surface, in particular we show that the system of relations between two sets of generators of theSU(2) group lead to a formulation of nonrelativistic spinone half theory on the sphereS3. First we examine various possibilities to extend this approach in the case of relativistic motion, then we give formulation for the Dirac and Maxwell equations in homogeneous space-time where a geometrical point is associated with the notion of relativistic top. Finally we formulate these equations in aS3 surface embedded inR5, using spherical system of coordinates, and examine the eigenvalue problem.