Yutaro Shoji: Regularization of Functional Determinants of Radial Operators via Heat Kernel Coefficients

Thursday 5 Jun 2025, 15:30 → 16:30 Europe/Ljubljana

https://zoom.us/j/3601731049?pwd=bVNQRjUxU2ExZ0cveWcxYXNUUGdjZz09 (A/1-106 - Seminarska soba fizike (F5))

The leading order quantum corrections in quantum field theory appear in the form of functional determinants, and their evaluation is very important in theoretical and phenomenological studies. We propose an efficient regularization method using the heat kernel coefficients. It enables us to regularize functional determinants in higher dimensions. In particular, our explicit formulas can regularize functional determinants in up to 13 dimensions, which has been a very difficult task before our study. The formulas can also be used to approximate higher angular momentum contributions in lower dimensions, which makes the numerical computation very efficient. The large angular momentum expansion of our formula gives the WKB formulas in the previous studies, but extended to higher orders. The results are obtained in both the zeta function regularization and the dimensional regularization.

hke.pdf