On the derivation of the formula for the Hamiltonian functional integral in theories with the first and second constraints

Simple and consistent derivation of the formula for the hamiltonian functional integral in theories with the first and second class constraints is given. The gauge conditions may be noninvolutive and the constraints and gauge conditions can be explicitely time-dependent. In contrast to other papers much attention is paid to prove the hamiltonian form of dynamics on the physical submanifold of the phase. It is shown that Δ-1 where Δ is the Faddeev - Popov determinant, is just the volume element in terms of noncanonical coordinates. The invariance of the final fomula for the functional integral under finite transformations of the gauge conditions is proved