Zeta-function regularization is uniquely defined and well

Zeta-function Regularization Is Uniquely Defined and Well

Hawking’s zeta function regularization procedure is shown to be rigorously and uniquely defined, thus putting and end to the spreading lore about different difficulties associated with it. Basic misconceptions, misunderstandings and errors which keep appearing in important scientific journals when dealing with this beautiful regularization method —and other analytical procedures— are clarified ...

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 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 ...

Fluctuations of Quantum Fields via Zeta Function Regularization

Explicit expressions for the expectation values and the variances of some observables, which are bilinear quantities in the quantum fields on a Ddimensional manifold, are derived making use of zeta function regularization. It is found that the variance, related to the second functional variation of the effective action, requires a further regularization and that the relative regularized varianc...

Non invariant zeta - function regularization in quantum Liouville theory 1

We consider two possible zeta-function regularization schemes of quantum Liouville theory. One refers to the Laplace-Beltrami operator covariant under conformal transformations, the other to the naive non invariant operator. The first produces an invariant regularization which however does not give rise to a theory invariant under the full conformal group. The other is equivalent to the regular...

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