F~,Y~MAN (i) originally noted the interesting result that, for quadratic actions, an average over all paths between fixed endpoints of the transition led to a separation of the quantum-mechanical transformation function into two factors. One factor depends upon the time interval of transition and the fixed endpoints, while the other factor is dependent upon the time interval alone. That is, for quadratic actions, FV, YN~AN argued that the general form for the quantum-mechanical transformation function or kernel is given by (~)