Diagrams for heat kernel expansions

A diagramatic heat kernel expansion technique is presented. The method is e specially well suited to the small-derivative expansion of the heat kernel, but it can also be used to reproduce the results obtained by the approach known as covariant perturbation theory. The new technique fives an expansio n for the heat kernel at coincident points. It can also be used to obtain t he derivative of the heat kernel, and this is useful for evaluating the exp ectation values of the stress-energy tensor.