  The extended commutation relations for a generalized uncertainty principle
have been based on the assumption of the minimal length in position. Instead of
this assumption, we start with a constrained Hamiltonian system described by
the conventional Poisson algebra and then impose appropriate second class
constraints to this system. Consequently, we can show that the consistent Dirac
brackets for this system are nothing but the extended commutation relations
describing the generalized uncertainty principle.

High Energy Physics - Theory