Zeta-Function Regularization, the Multiplicative Anomaly and the Wodzicki Residue

Abstract:

The multiplicative anomaly associated with the zeta-function regularized determinant is computed for the Laplace-type operators V ₁=−Δ+V ₁ and V ₂=−Δ+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.