The Higher Derivative Expansion of the Effective Action by the String-Inspired Method, Part I

The higher derivative expansion of the one-loop effective action for an external scalar potential is calculated to order O(T**7), using the string-inspired Bern-Kosower method in the first quantized path integral formulation. Comparisons are made with standard heat kernel calculations and with the corresponding Feynman diagrammatic calculation in order to show the efficiency of the present method.