Related papers: Local $\zeta$-function techniques vs point-splitti…
We conclude the rigorous analysis of a previous paper concerning the relation between the (Euclidean) point-splitting approach and the local $\zeta$-function procedure to renormalize physical quantities at one-loop in (Euclidean) QFT in…
In this article we introduce a new type of local zeta functions and study some connections with pseudodifferential operators in the framework of non-Archimedean fields. The new local zeta functions are defined by integrating complex powers…
This is a quick review on some technology concerning the local zeta function applied to Quantum Field Theory in curved static (thermal) spacetime to regularize the stress-energy tensor and the field fluctuations.
A method to regularize and renormalize the fluctuations of a quantum field in a curved background in the $\zeta$-function approach is presented. The method produces finite quantities directly and finite scale-parametrized counterterms at…
Some recent (1997-1998) theoretical results concerning the $\zeta$-function regularization procedure used to renormalize, at one-loop, the effective Lagrangian, the field fluctuations and the stress-tensor in curved spacetime are reviewed.
A review of some recent advances in zeta function techniques is given, in problems of pure mathematical nature but also as applied to the computation of quantum vacuum fluctuations in different field theories, and specially with a view to…
In this article, we introduce a notion of non-degeneracy, with respect to certain Newton polyhedra, for rational functions over non-Archimedean locals fields of arbitrary characteristic. We study the local zeta functions attached to…
We express the zeta function associated to the Laplacian operator on $S^1_r\times M$ in terms of the zeta function associated to the Laplacian on $M$, where $M$ is a compact connected Riemannian manifold. This gives formulas for the…
The Laplace operator acting on antisymmetric tensor fields in a $D$--dimensional Euclidean ball is studied. Gauge-invariant local boundary conditions (absolute and relative ones, in the language of Gilkey) are considered. The eigenfuctions…
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…
We prove that the zeta-function $\zeta_\Delta$ of the Laplacian $\Delta$ on a self-similar fractals with spectral decimation admits a meromorphic continuation to the whole complex plane. We characterise the poles, compute their residues,…
In this article, we study local zeta functions over non-Archimedean locals fields of arbitrary characteristic attached to rational functions and characters $\chi$ of the units of the ring of integers $\mathcal{O}_{K}$, by using an approach…
The effective potentials for massless scalar and vector quantum field theories on D dimensional manifolds with p compact noncommutative extra dimensions are evaluated by means of dimensional regularization implemented by zeta function…
In the 70's Igusa developed a uniform theory for local zeta functions and oscillatory integrals attached to polynomials with coefficients in a local field of characteristic zero. In the present article this theory is extended to the case of…
Partial zeta functions of algebraic varieties over finite fields generalize the classical zeta function by allowing each variable to be defined over a possibly different extension field of a fixed finite field. Due to this extra variation…
It is known that local zeta functions associated with real analytic functions can be analytically continued as meromorphic functions to the hole complex plane. In this paper, certain cases of specific (non-real analytic) smooth functions…
We introduce a new method which enables us to calculate the coefficients of the poles of local zeta functions very precisely and prove some explicit formulas. Some vanishing theorems for the candidate poles of local zeta functions will be…
To motivate our discussion, we consider a 1+1 dimensional scalar field interacting with a static Coulomb-type background, so that the spectrum of quantum fluctuations is given by a second-order differential operator on a single coordinate r…
Heat-kernel expansion and zeta function regularisation are discussed for Laplace type operators with discrete spectrum in non compact domains. Since a general theory is lacking, the heat-kernel expansion is investigated by means of several…
In this paper we study the spectral asymmetry of (possibly nonselfadjoint) elliptic PsiDO's in terms of the difference of zeta functions coming from different cuttings. Refining previous formulas of Wodzicki in the case of odd class…