2025/12/03 by Barvinsky, Andrei O., Kalugin, Alexey E., Wachowski, Władysław · 1 citation
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2512.03944
We consider integral kernels for functions f( F) of a minimal second-order differential operator F(∇) on a curved spacetime. We show that they can be expanded in a functional series, analogous to the DeWitt expansion for the heat kernel, by integrating the latter term-by-term. This procedure leads to a separation of two types of data: all information about the bundle geometry and the operator F(∇) is still contained in the standard HaMiDeW coefficients ak[F | x,x'] (we call this property ``off-diagonal functoriality''), while information about the function f is encoded in some new scalar functions \mathbbBα[f | σ] and \mathbbWα[f | σ, m2], which we call basis and complete massive kernels, respectively. These objects are calculated for operator functions of the form exp(-τ Fν)/( Fμ+ λ) as multiple Mellin--Barnes integrals. The article also discusses subtle issues such as the validity of the term-by-term integration, the regularization of IR divergent integrals, and the physical interpretation of the resulting expansions.