Related papers: Zimmermann's Forest Formula, Infrared Divergences …
The present work contains a consistent formulation of the methods of dimensional regularization (DimReg) and minimal subtraction (MS) in Minkowski position space. The methods are implemented into the framework of perturbative Algebraic…
The properties of the Lyman-$\alpha$ absorptions observed in the spectra of QSOs are reviewed: the distribution of column densities and Doppler widths, the redshift evolution, the ``inverse effect'', the clustering. By interpreting the…
We consider the infrared and ultraviolet behaviour of the effective quantum field theory of a single $Z_2$ symmetric scalar field. In a previous paper we proved to all orders in perturbation theory the renormalizability of massive effective…
We propose a renormalon-inspired resummation of QCD perturbation theory based on approximating the renormalization scheme (RS) invariant effective charge beta-function coefficients by the portion containing the highest power of…
In this paper, we study the uniform H\"older continuity of the generalized Riemann function $R_{\alpha,\beta}$ (with $\alpha>1$ and $\beta>0$) defined by \[ R_{\alpha,\beta}(x)=\sum_{n=1}^{+\infty}\frac{\sin(\pi n^\beta x)}{n^\alpha},\quad…
Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two…
We analyze critically the renormalization of quantum fields in cosmological spacetimes, using non covariant ultraviolet cutoffs. We compute explicitly the counterterms necessary to renormalize the semiclassical Einstein equations, using…
The usual Bogolyubov R-operation works in non-renormalizable theories in the same way as in renormalizable ones. However, in the non-renormalizable case, the counter-terms eliminating ultraviolet divergences do not repeat the structure of…
Using differential renormalization, we calculate the complete two-point function of the background gauge superfield in pure N=1 Supersymmetric Yang-Mills theory to two loops. Ultraviolet and (off-shell) infrared divergences are renormalized…
In this paper, we construct the beta function in the functorial formulation of two-dimensional quantum field theories (FQFT). A key feature of this approach is the absence of ultraviolet divergences. We show that, nevertheless, in the FQFT…
The resummed expression for the quark form factor illustrates the fact that dimensional continuation provides a regularization not only for ultraviolet and infrared singularities of fixed order QCD amplitudes, but also for the Landau pole…
We construct a non-formal deformation machinery for the actions of the Heisenberg supergroup analogue to the one developed by M. Rieffel for the actions of R^d. However, the method used here differs from Rieffel's one: we obtain a Universal…
The vacuum expectation value of the evolution operator for a general class of Hamiltonians used in quantum field theory and statistical physics and which include unstable particles is considered. An exact formula which describes the large…
This paper derives a unifying theorem establishing consistency results for a broad class of tree-based algorithms. It improves current results in two aspects. First of all, it can be applied to algorithms that vary from traditional Random…
Renormalization is a well-known technique to get rid of ultraviolet (UV) singularities. When relying on Dimensional Regularization (DREG), these become manifest as $\epsilon$-poles, allowing to define counter-terms with useful recursive…
A stochastic process with self-interaction as a model of quantum field theory is studied. We consider an Ornstein-Uhlenbeck stochastic process x(t) with interaction of the form x^{(\alpha)}(t)^4, where $\alpha$ indicates the fractional…
This PhD thesis is devoted to show that differential renormalization is a simple and useful renormalization method that we can use when dealing with gauge theories. In this work, it is shown how the one-loop results of Constraint…
We give a non-perturbative proof of a gradient formula for beta functions of two-dimensional quantum field theories. The gradient formula has the form \partial_{i}c = - (g_{ij}+\Delta g_{ij} +b_{ij})\beta^{j} where \beta^{j} are the beta…
We discuss the implementation of Bayesian inversion methods in order to recover the properties of the intergalactic medium from observations of the neutral hydrogen Lyman-$\alpha$ absorptions observed in the spectra of high redshift quasars…
Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two…