  In the approach to the geometric quantization, based on the conversion of
second-class constraints, we resolve the respective non-linear zero curvature
conditions for the extended symplectic potential. From the zero curvature
conditions, we deduce new, linear, equations for the extended symplectic
potential. Then we show that being the linear equations satisfied, their
solution does certainly satisfy the non-linear zero curvature condition, as
well. Finally, we give the functional resolution to the new linear equations,
and then deduce the respective path integral representation. We do our
consideration as to the general case of a phase superspace where both Boson and
Fermion coordinates are present on equal footing.

High Energy Physics - Theory