Quantum effects of classical phase space singularities in lattice gauge models

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Gauge theories are the proper tool for describing the fundamental interactions between elementary particles. In the framework of renormalized perturbation theory, they reproduce the experimental data with extraordinary precision. There are however several phenomena which cannot be treated satisfactorily by means of perturbation theory, like the Gribov problem, certain anomalies, quark confinement or, more generally, the existence of bound states. To enter the discussion of such phenomena, one needs a deeper understanding of the mathematical structure of gauge theories. Important aspects of this structure become manifest in the gauge orbit space, that is, the space of the physical degrees of freedom of the theory. Since the gauge orbit space is the quotient of a group action, it may contain singularities. It is a long-standing problem to clarify the role of these singularities in quantum theory. In the present project, this problem shall be studied systematically for SU(2)-lattice gauge models by means of a method which was developed recently by the author and others.