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arXiv · hep-th/9701060

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

E. Elizalde·L. Vanzo·S. Zerbini
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Abstract

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.

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E. Elizalde, L. Vanzo, S. Zerbini. 1997-11-07. Zeta-function regularization, the multiplicative anomaly and the Wodzicki residue. https://doi.org/10.1007/s002200050371

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