Geometry of the physical phase space in quantum gauge systems

The physical phase space in gauge systems is studied. Simple soluble gauge models are considered in detail. Effects caused by a non-Euclidean geometry of the physical phase space in quantum gauge models are described in the operator and path integral formalisms. The projection on the Dirac gauge invariant states is used to derive a necessary modification of the Hamiltonian path integral in gauge theories of the Yang–Mills type with fermions that takes into account the non-Euclidean geometry of the physical phase space. The new path integral is applied to resolve the Gribov obstruction. Applications to the Kogut–Susskind lattice gauge theory are given. The basic ideas are illustrated with examples accessible for non-specialists.