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 λ dropped out of the extended Hamiltonian. Since φ 1 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 λ, which has ceased to have any effect on the particle's dynamics. Therefore, that λ dropped out of the Hamiltonian, that u 1 is undetermined, and that φ 1 = p λ is first class, are all closely interrelated.