  There exists a simple rule by which path integrals for the motion of a point
particle in a flat space can be transformed correctly into those in curved
space. This rule arose from well-established methods in the theory of plastic
deformations, where crystals with defects are described mathematically by
applying nonholonomic coordinate transformations to ideal crystals. In the
context of time-sliced path integrals, this has given rise to a {\em quantum
equivalence principle\/} which determines the measure of fluctating orbits in
spaces with curvature and torsion. The nonholonomic transformations are
accompanied by a nontrivial Jacobian which in curved spaces produces an
additional energy proportional to the curvature scalar, thereby canceling an
equal term found earlier by DeWitt from a naive formulation of Feynman's
time-sliced path integral in curved space. The importance of this cancelation
has been documented in various systems (H-atom, particle on the surface of a
sphere, spinning top). Here we point out its relevance in the process of
bosonizing a nonabelian one-dimensional quantum field theory, whose fields live
in a flat field space. Its bosonized version is a quantum-mechanical path
integral of a point particle moving in a space with constant curvature. The
additional term introduced by the Jacobian is crucial for the identity between
original and bosonized theory.
  A useful bozonization tool is the so-called Hubbard-Stratonovich formula for
which we find a nonabelian version.
