The geometrical interpretation of the Faddeev–Popov determinant in Polyakov’s theory of random surfaces

Abstract

In the context of Polyakov’s theory the geometrical approach, in which the functional measure is defined as a formal volume ∞-form, is developed. The special version of the Fubini theorem on manifolds is derived, which provides the geometrical interpretation of the Faddeev–Popov method. The conformal gauge is studied within this framework. As a result, the explicit form of functional measure in effective Liouville quantum field theory is obtained.