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It is shown that quantum one-loop potentials of the bulk fields in theRandall and Sundrum (RS) model may be immediately expressed in integrals withuse of Barvinsky-Nesterov or equivalently Gelfand-Yaglom methods of calculationof quantum determinants. Simple expression is obtained for the UV-finitedifference of one-loop quantum energies for two arbitrary values of parameterof the double-trace asymptotic boundary condition in one-brane and two-braneRS-models. Compact formula for Schwinger-DeWitt expansion gives values ofinduced Planck mass and induced gauge coupling constant in transverse space.S-DW expansion is plagued by IR-divergences in one-brane RS-model and makessense in two-brane model.

Scalar field on AdS: quantum one loop "in one line"