Evaluation of functional integrals around a continuous set of important field configurations

For euclidean functional integrals, the relevance of configurations beyond the set of classical solutions is investigated. We propose an equation to select the important configurations and derive general expressions for their contribution to the integral. Employing a pseudoparticle picture, we perform a dilute-gas approximation and estimate finite-density corrections through a virial expansion. The methods are exemplified for the anharmonic oscillator and the double well potential.