Quantum mechanics of systems with a gauge group

In constructing descriptions of gauge models of elementary particle physics in terms of invariant variables restrictions for configuration and phase space of these variables arise. These restrictions were not taken into account in formulations of the models on the basis of continual integral. It is shown by the example of mechanical models with arbitrary gauge group how the Hamiltonian continual integral should be modified when the structure of the configuration and phase spaces is modified. Physical interpretation of this phenomenon is suggested. The result is obtained on the basis of the Dirac scheme for the quantization of systems with constraints and is equivalent to this scheme.