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

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

1997-01-14

arxiv.org/abs/hep-th/9701060v2

Commun.Math.Phys. 194 (1998) 613-630

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 17 pages, 3 figures. Small corrections, two new formulas, and an addition to the references. To appear in Commun. Math.

Scientific paper

10.1007/s002200050371

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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