Regularization of Functional Determinants of Radial Operators via Heat Kernel Coefficients

Abstract: We propose an efficient regularization method for functional determinants of radial operators using heat kernel coefficients. Our key finding is a systematic way to identify heat kernel coefficients in the angular momentum space. We explicitly obtain the formulas up to sixth order in the heat kernel expansion, which suffice to regularize functional determinants in up to 13 dimensions. We find that the heat kernel coefficients accurately approximate the large angular momentum dependence of functional determinants, and make numerical computations more efficient. In the limit of a large angular momentum, our formulas reduce to the WKB formulas in previous studies, but extended to higher orders. All the results are available in both the zeta function regularization and the dimensional regularization.