Local structure of functional spaces and dynamical variables of gauge-invariant fields

The local structure of the functional spaces of gauge-invariant fields is considered. The variables of the functional spaces are classified as fictitious, dynamical, and “Iongitudinal”. In particular, one can have gauge fields that do not contain dynamical variables at all although the interaction of dynamical fields can be realized by means of them (threedimensional gravitation, two-dimensional electrodynamics). The mathematical origin of this phenomenon is elucidated. The dynamical and “longitudinal” variables are analyzed in four-dimensional gravitation and electrodynamics.