Zeta-function regularization, the multiplicative anomaly and the Wodzicki residue

The multiplicative anomaly associated with the zeta-function regularized determinant is computed for the Laplace-type operators L_1=-\lap+V_1 and L_2=-\lap+V_2, with $V_1$, $V_2$ constant, in a D-dimensional compact smooth manifold $M_D$, making use of several results due to Wodzicki and by direct calculations in some explicit examples. It is found that the multiplicative anomaly is vanishing for $D$ odd and for D=2. An application to the one-loop effective potential of the O(2) self-interacting scalar model is outlined.Comment: LaTeX, 17 pages, 3 figures. Small corrections, two new formulas, and an addition to the references. To appear in Commun. Math. Phy

Hawking Radiation as Tunneling: the D-dimensional rotating case

The tunneling method for the Hawking radiation is revisited and applied to the $D$ dimensional rotating case. Emphasis is given to covariance of results. Certain ambiguities afflicting the procedure are resolved.Comment: Talk delivered at the Seventh International Workshop Quantum Field Theory under the influence of External Conditions, QFEXT'05, september 05,Barcelona, Spain. To appear in Journal of Phys.