Related papers: Renormalons as dilatation modes in the functional …
We explore the possibilities of using the fermionic functional renormalization group to compute the phase diagram of systems with competing instabilities. In order to overcome the ubiquituous divergences encountered in RG flows, we propose…
A simple formal procedure makes the main properties of the lagrangian binomial extendable to functions depending to any kind of order of the time--derivatives of the lagrangian coordinates. Such a broadly formulated binomial can provide the…
We consider the large order behavior of the perturbative expansion of the scalar $\varphi^4$ field theory in terms of a perturbative expansion around an instanton solution. We have computed the series of the free energy up to two-loop order…
Higher orders in perturbation theory require the calculation of Feynman integrals at multiple loops. We report on an approach to systematically solve Feynman integrals by means of symbolic summation and discuss the underlying algorithms.…
We continue the development of a position space approach to equations for Feynman multi-loop integrals. The key idea of the approach is that unintegrated products of Greens functions in position space are still loop integral in momentum…
Renormalization factors for local vector and axial vector currents for the Wilson quark action are perturbatively calculated to one loop order including finite quark masses from the ratio of the on-shell quark matrix elements in the Feynman…
Perturbative series of some quantities in quantum field theories, such as the pole mass of a quark, suffer from a kind of divergence called renormalon divergence. In this paper, the leading renormalon in the pole mass is investigated, and a…
Nonlinear perturbation of Fuchsian systems are studied in a region including two singularities. It is proved that such systems are generally not analytically equivalent to their linear part (they are not linearizable) and the obstructions…
Two-loop Feynman integrals of the massive $\phi^4_d$ field theory are explicitly obtained for generic space dimensions $d$. Corresponding renormalization-group functions are expressed in a compact form in terms of Gauss hypergeometric…
Quantum physics has revealed many interesting formal properties associated with the algebra of two operators, A and B, satisfying the partial commutation relation AB-BA=1. This study surveys the relationships between classical combinatorial…
We describe differential forms representing Feynman amplitudes in configuration spaces of Feynman graphs, and regularization and evaluation techniques, for suitable chains of integration, that give rise to periods of mixed Tate motives.
The aim of this paper is to describe how to use regularization and renormalization to construct a perturbative quantum field theory from a Lagrangian. We first define renormalizations and Feynman measures, and show that although there need…
Fast-growing hierarchies are sequences of functions obtained through various processes similar to the ones that yield multiplication from addition, exponentiation from multiplication, etc. We observe that fast-growing hierarchies can be…
In order that current and future renormalon results in QCD can be used to their full advantage it is important to understand how the Borel transforms of related functions are themselves related. For example, a change of renormalisation…
Starting from a representation of the early time evolution of a dynamical system in terms of the polynomial expression of some observable f (t) as a function of the time variable in some interval 0 < t < T, we investigate how to…
Many extended chemical and biological systems self-organise into complex patterns that drive the medium behaviour in a non-linear fashion. An important class of such systems are excitable media, including neural and cardiac tissues. In…
In the first part of this lecture, the 1/N expansion technique is illustrated for the case of the large-N sigma model. In large-N gauge theories, the 1/N expansion is tantamount to sorting the Feynman diagrams according to their degree of…
We investigate multicritical phenomena in O(N)+O(M)-models by means of nonperturbative renormalization group equations. This constitutes an elementary building block for the study of competing orders in a variety of physical systems. To…
In this paper we investigate the normal and the large fluctuations of additive functionals associated with a stochastic process under a general non-Poissonian resetting mechanism. Cumulative functionals of regenerative processes are very…
The problem of large order behaviour of perturbation theory for quantum mechanical systems is considered. A new approach to it is developed. An explicit mechanism showing the connection between large order recursive relations and classical…