Abstract
A study is made of the path integral quantization for a D-dimensional sphere as an example of constrained systems by means of the Faddeev-Senjanovic formula, although no one has checked its validity with paying attentions to a global structure of integration regions. By adopting a well-defined path measure obtained through the time discretization and applying formulas of spherical harmonics, operator Hamiltonians can be picked out from their formula without recourse to any approximation such as a semi-classical one ( h → 0). The analysis is made with a model, H=C p 2+M 2C 2 . We might thus regard the path integral formula of Faddeev-Senjanovic as a powerful breakthrough to “quantum” constrained systems where ordinary canonical approaches sometimes encounter difficulties in giving well-defined canonical momenta because of the uncertainty principle.
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