Abstract
The global aspects of the gauge fixing in the Polyakov path integral for the bosonic string are considered within the Ebin–Fischer–Mareden approach to the geometry of spaces of Riemannian metrics and conformal structures. It is shown that for surfaces of higher genus, the existence of local conformal gauges is sufficient to derive the globally defined integral over the Teichmüller space. The generalized Faddeev–Popov procedure for incomplete gauges is formulated and used to derive the global expression for the Polyakov path integral in the cases of torus and sphere. The Gribov ambiguity in the functional integral over surfaces without boundary can be successfully overcome for arbitrary genus.
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