  We recall the successes of the Hubbard-Stratonovich Transformation (HST) of
many-body theory, point out its failure to cope with competing channels of
collective phenomena and show how to overcome this by Variational Perturbation
Theory. That yields exponentially fast converging results, thanks to the help
of a variety of {\it collective classical fields}, rather than a fluctuating
{\it collective quantum field} as suggested by the HST.
