Abstract: The heat-kernel formalism is a powerful and versatile tool for analyzing one-loop divergences and asymptotic behaviors of the effective action. After briefly reviewing its standard formulation, we present a more intuitive approach that avoids relying on an ansatz for solving the associated Schrödinger-type equation. Our method leverages Zassenhaus’ formula to treat exponentials of noncommuting operators in a systematic way. Furthermore, we develop a direct configuration-space procedure for…