Irreducible representations of Dirac algebra for a constrained system

All possible irreducible representations of the Dirac algebra for a particle constrained to move on a D-dimensional manifold f (x) 0 are explicitly constructed in terms of canonical operators (x) over cap (alpha), (π) over cap (alpha) (alpha = 1, 2, D + 1) in R D,1; by assuming that the manifold, which is embedded in RD+1, is diffeomorphic to S-D. It is shown that for D = 1 any irreducible representation,is uniquely specified by a real parameter alpha belonging to [0, 1), while for D greater than or equal to 2 the irreducible representation is unique. The explicit form of inner products in (x) over cap (alpha)-diagonal representation is given with the help of auxiliary wavefunctions on RD+1, provided that they satisfy certain boundary conditions on the manifold. Applying it we further examine the hermiticity property of the fundamental operators of the Dirac algebra.