The smearing function from the functional renormalization group

Abstract

Abstract The smearing function has been proposed as a tool for writing down the one-loop correction to the Wilsonian effective action in the form of the Schwinger proper-time representation of the functional determinant. Due to the fact that the existence of the smearing function is only a postulate, it is interesting to explore if it is possible to obtain such a function from the functional renormalization group, which is a closely related formulation. In this work, we show that it is possible to obtain the smearing function from the functional renormalization group only in a special case, but not in general cases.