Zeta - function Regularization , the Multiplicative Anomaly and the Wodzicki Residue
نویسندگان
چکیده
The multiplicative anomaly associated with the zeta-function regularized determinant is computed for the Laplace-type operators L1 = −∆+ V1 and L2 = −∆+ V2, with V1, V2 constant, in a D-dimensional compact smooth manifold MD, 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. PACS numbers: 04.62.+v, 04.70.Dy Running title: Zetas, multiplicative anomaly and Wodzicki residue
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