"In the sixties, a new field of applications of functional integrals appeared — the quantization of gauge fields. The electromagnetic field, the Einstein gravitational field, the Yang-Mills field and the chiral field can serve as examples of gauge fields. The action functionals of those fields are invariant under gauge transformations which depend on one or several arbitrary functions. From a mathematical point of view, gauge fields are fields of geometrical origin which are connected with fibrations over four-dimensional space-time. The specificity of geometrical fields has to be taken into account when quantizing them; otherwise incorrect results may be obtained."