  A simple mapping procedure is presented by which classical orbits and path
integrals for the motion of a point particle in flat space can be transformed
directly into those in curved space with torsion. Our procedure evolved from
well-established methods in the theory of plastic deformations, where crystals
with defects are described mathematically as images of ideal crystals under
active nonholonomic coordinate transformations.
  Our mapping procedure may be viewed as a natural extension of Einstein's
famous equivalence principle. When applied to time-sliced path integrals, it
gives rise to a new "quantum equivalence principle" which determines short-time
action and measure of fluctuating orbits in spaces with curvature and torsion.
The nonholonomic transformations possesses a nontrivial Jacobian in the path
measure which produces in a curved space an additional term proportional to the
curvature scalar R, thus canceling a similar term found earlier by DeWitt. This
cancelation is important for correctly describing semiclassically and quantum
mechanically various systems such as the hydrogen atom, a particle on the
surface of a sphere, and a spinning top. It is also indispensable for the
process of bosonization, by which Fermi particles are redescribed by those
fields.
