Related papers: An etude on a renormalization
Discrete amorphous materials are best described in terms of arbitrary networks which can be embedded in three dimensional space. Investigating the thermodynamic equilibrium as well as non-equilibrium behavior of such materials around second…
We first briefly review some aspects of the techniques of dealing with ultraviolet divergences in Feynman amplitudes in an Euclidian $D$-dimensional space-time. Next we consider compactification of a $d$-dimensional ($d\leq D$) subspace.…
This paper contains a short and simplified proof of desingularization over fields of characteristic zero, together with various applications to other problems in algebraic geometry (among others, the study of the behavior of…
We propose a new approach to the theory of normal forms for Hamiltonian systems near a non-resonant elliptic singular point. We consider the space of all Hamiltonian functions with such an equilibrium position at the origin and construct a…
The inherent ill-posed nature of image reconstruction problems, due to limitations in the physical acquisition process, is typically addressed by introducing a regularisation term that incorporates prior knowledge about the underlying…
In this study, we delve into the intricate mathematical frameworks essential for the renormalization of effective elastic models within complex physical systems. By integrating advanced tools such as Laurent series, residue theorem, winding…
We illustrate how to extend the concept of structural stability through applying it to the front propagation speed selection problem. This consideration leads us to a renormalization group study of the problem. The study illustrates two…
In this paper we present a method to deal with divergences in perturbation theory using the method of the Zeta regularization, first of all we use the Euler-Mc Laurin Sum formula to associate the divergent integral to a divergent sum in the…
A divergence-free approach to relativistic quantum electrodynamics based on regularisation of equations of quantum mechanics is discussed. This approach is shown to be exactly equivalent to the conventional Feynman-Dyson renormalisation…
We present a renormalization group (RG) procedure which works naturally on a wide class of interacting one-dimension models based on perturbed (possibly strongly) continuum conformal and integrable models. This procedure integrates Kenneth…
We present a general analysis of the field theoretical properties which guarantee the recovery, at the renormalized level, of symmetries broken by regularization. We also discuss the anomalous case.
Proceeding by way of examples, we update the combinatorics of the treatment of Feynman diagrams with subdivergences in differential renormalization from more recent viewpoints in Epstein--Glaser renormalization in $x$-space.
A recently proposed renormalization scheme can be used to deal with nonrelativistic potential scattering exhibiting ultraviolet divergence in momentum space. A numerical application of this scheme is made in the case of potential scattering…
We investigate the consistency of the background-field formalism when applying various regularizations and renormalization schemes. By an example of a two-dimensional $\sigma$ model it is demonstrated that the background-field method gives…
Using resummation in perturbation theories at finite temperature or in non-equilibrium is unavoidable to obtain consistent results. Resummation, however, is often in conflict with renormalization. In this talk we give two possible solutions…
The singular behavior of conformal interactions is examined within a comparative analysis of renormalization frameworks. The effective approach--inspired by the effective-field theory program--and its connection with the core framework are…
We describe the equivalence at one loop between constrained differential renormalization and regularization by dimensional reduction in the MS scheme. To illustrate it, we reexamine the calculation of supergravity corrections to (g-2)_l.
The study of nonlinear phenomena in systems with many degrees of freedom often relies on complex numerical simulations. In trying to model realistic situations, these systems may be coupled to an external environment which drives their…
Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…
It is shown that the renormalization group method does not necessarily eliminate all secular terms in perturbation series to partial differential equations and a functional subspace of renormalizable secular solutions corresponds to a…