Simple way to calculate UV-finite one-loop quantum energy in Randall-Sundrum model

Abstract

The surprising simplicity of Barvinsky-Nesterov or equivalently Gelfand-Yaglom methods of calculation of quantum determinants permits to obtain compact expressions for UV-finite difference of one-loop quantum energies for two arbitrary values of parameter of the double-trace asymptotic boundary conditions. This result generalizes Gubser and Mitra calculation for particular case of difference of "regular" and "irregular" one-loop energies in one-brane RS-model. Approach developed in the paper also allows to get "in one line" the one-loop quantum energies in two-brane RS-model. The relationship between "one-loop" expressions corresponding to mixed Robin and to double-trace asymptotic boundary conditions is traced.