Related papers: Zero-point energies and the multiplicative anomaly
In the framework leading to the multiplicative anomaly formula ---which is here proven to be valid even in cases of known spectrum but non-compact manifold (very important in Physics)--- zeta-function regularisation techniques are shown to…
We discuss the role of the multiplicative anomaly for a complex scalar field at finite temperature and density. It is argued that physical considerations must be applied to determine which of the many possible expressions for the effective…
An explicit formula to compute the multiplicative anomaly or defect of $\zeta$-regularized products of linear factors is derived, by using a Feynman parametrization, generalizing Shintani-Mizuno formulas. Firstly, this is applied on…
The relativistic complex scalar field at finite temperature and in presence of a net conserved charge is studied in reference to recent developments on the multiplicative anomaly. This quantity, overlooked until now, is computed and it is…
In a recent work, S. Dowker has shed doubt on a recipe used in computing the partition function for a matrix valued operator. This recipe, advocated by Benson, Bernstein and Dodelson, leads naturally to the so called multiplicative anomaly…
When dealing with zeta-function regularized functional determinants of matrix valued differential operators, an additional term, overlooked until now and due to the multiplicative anomaly, may arise. The presence and physical relevance of…
Observing that the logarithm of a product of two elliptic operators differs from the sum of the logarithms by a finite sum of operator brackets, we infer that regularised traces of this difference are local as finite sums of noncommutative…
We show that the long-standing problem of gauge dependence of the effective potential arises due to the factorisation of the determinant of operators, which is invalid when we take the zeta-regularised trace of the operators. We show by…
Some aspects of the multiplicative anomaly of zeta determinants are investigated. A rather simple approach is adopted and, in particular, the question of zeta function factorization, together with its possible relation with the…
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 $…
After a brief survey of zeta function regularization issues and of the related multiplicative anomaly, illustrated with a couple of basic examples, namely the harmonic oscillator and quantum field theory at finite temperature, an…
A brief survey of the zeta function regularization and multiplicative anomaly issues when the associated zeta function of fluctuation operator is the regular at the origin (regular case) as well as when it is singular at the origin…
In this paper, the problem of multiplicative anomaly of zeta regularization is solved for polynomials. For a regularizable sequence $\Lambda$, we explicitly calculate the zeta regularized product of $(\Lambda-z_1)\dots(\Lambda-z_n)$ for…
The global additive and multiplicative properties of Laplace type operators acting on irreducible rank 1 symmetric spaces are considered. The explicit form of the zeta function on product spaces and of the multiplicative anomaly is derived.
The global multiplicative properties of Laplace type operators acting on irreducible rank one symmetric spaces are considered. The explicit form of the multiplicative anomaly is derived and its corresponding value is calculated exactly, for…
The one-loop effective action for a generic set of quantum fields is calculared as a nonlocal expansion in powers of the curvatures (field strengths). This expansion is obtained to third order in the curvature. It is stressed that the…
The first quantum correction to the finite temperature partition function for a self-interacting massless scalar field on a $D-$dimensional flat manifold with $p$ non-commutative extra dimensions is evaluated by means of dimensional…
Elizalde, Vanzo, and Zerbini have shown that the effective action of two free Euclidean scalar fields in flat space contains a `multiplicative anomaly' when zeta-function regularization is used. This is related to the Wodzicki residue. I…
The one-loop effective action for a scalar field defined in the ultrastatic space-time where non standard logarithmic terms in the asymptotic heat-kernel expansion are present, is investigated by a generalisation of zeta-function…
The functional determinant multiplicative anomaly, or defect, is more closely investigated and explicit forms for products of linear operators are produced. I also present formulae for the defect of products of second order operators in…