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 sphereS ³. 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 aS ³ surface embedded inR ⁵, using spherical system of coordinates, and examine the eigenvalue problem.