Hamiltonian Quantization with Constraints
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In the framework of the Dirac quantization with the second class constraints, a free particle moving on surface of (d − 1)-dimensional sphere has ambiguity in its energy spectrum due arbitrary shift of canonical momenta. In this chapter, we show that this spectrum obtained by the Dirac method can be consistent with that of the improved Dirac Hamiltonian formalism at the level of the first class constraint by fixing ambiguity, and then we discuss its physical consequences . We next study a free particle system residing on torus to investigate its first class Hamiltonian associated with its Stückelberg coordinates .