Nonperturbative Effects in Quantum Field Theory on Curved Spaces

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Abstract
The quantum continuum action for gauge theories in two dimensions is constructed in the axial gauge. For non-Abelian groups the action differs from the usual expectations by nonperturbative, noncoercive corrections, whose role is to ensure gauge invariance for the quantum field theory outside of perturbation theory. Consequently, ordinary perturbation theory and semiclassical approximations become inapplicable. Similar conclusions are expected to apply in more dimensions.