Generating functionals for harmonic expectation values of paths with fixedend points: Feynman diagrams for nonpolynomial interactions

We introduce a general class of generating functionals for the calculation of quantum-mechanical expectation values of arbitrary functionals of fluctu ating paths with fixed end points in configuration or momentum space. The g enerating functionals are calculated explicitly for the harmonic oscillator with time-dependent frequency, and used to derive a smearing formula for c orrelation functions of polynomial and nonpolynomial functions of time-depe ndent positions and momenta. This formula summarizes the effect of quantum fluctuations, and serves to derive generalized Wick rules and Feynman diagr ams for perturbation expansions of nonpolynomial interactions. [S1063-651X( 99)04508-0].