Irreducible Representations of Fundamental Algebra for Quantum Mechanics on S D and Gauge Structures

All possible irreducible representations of fundamental algebra for a particle moving on SD are determined by applying the induced representation technique developed by Wigner. It is shown that the theory is automatically equipped with a monopole-like gauge potential. Some topological properties of the gauge potential are also discussed. Examining a relation of our theory with Dirac’s formulation for a constrained system we determine the irreducible representation of the Dirac algebra for a particle constrained on SD.