Abstract
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 ?, ? (? = 1, 2, ..., D + 1) in D+1 by assuming that the manifold, which is embedded in D+1, is diffeomorphic to SD. It is shown that for D = 1 any irreducible representation is uniquely specified by a real parameter ? belonging to [0, 1), while for D ? 2 the irreducible representation is unique. The explicit form of inner products in ?-diagonal representation is given with the help of auxiliary wavefunctions on D+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.
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