Examination of the above Hamiltonian shows a number of interesting things happening. One thing to note is that, on-shell when the constraints are satisfied, the extended Hamiltonian is identical to the naive Hamiltonian, as required. Also, note that dropped out of the extended Hamiltonian. Since is a first class primary constraint, it should be interpreted as a generator of a gauge transformation. The gauge freedom is the freedom to choose , which has ceased to have any effect on the particle's dynamics. Therefore, that dropped out of the Hamiltonian, that 1 is undetermined, and that = "pλ" is first class, are all closely interrelated.