LOOP CALCULATIONS IN QUANTUM-MECHANICAL NONLINEAR SIGMA-MODELS

By carefully analyzing the relations between operator methods and the discretized and continuum path integral formulations of quantum-mechan ical systems, we have found the correct Feynman rules for one-dimensio nal path integrals in curved spacetime. Although the prescription how to deal with the products of distributions that appear in the computat ion of Feynman diagrams in configuration space is surprising, this pre scription follows unambiguously from the discretized path integral. We check our results by an explicit two-loop calculation.