Related papers: Renormalisation scheme for vector fields on T2 wit…
Recently \cite{Horowitz:2022rpp,Horowitz:2022uak}, denominator regularisation (Den. Reg.) scheme has been proposed to handle divergences in quantum field theory. It is shown to yield results as simple as in dimensional regularisation scheme…
In this letter we numerically investigate the merging mechanism between two clusters of point vortices. We introduce a concept of renormalized Onsager function, an elaboration of the solutions of the mean field equation, and use it to…
In part I general aspects of the renormalization of a spontaneously broken gauge theory have been introduced. Here, in part II, two-loop renormalization is introduced and discussed within the context of the minimal Standard Model.…
We apply an analytic description to the inclusive decay of the $\tau$ lepton. We argue that this method gives not only a self-consistent description of the process both in the timelike region by using the initial expression for $R_\tau$ and…
We write spectral decomposition of the hypergeometric differential operator on the contour $Re z=1/2$ (multiplicity of spectrum is 2). As a result, we obtain an integral transform that differs from the Jacobi (or Olevsky) transform. We also…
The renormalization group flow of an integrable two dimensional quantum field theory which contains unstable particles is investigated. The analysis is carried out for the Virasoro central charge and the conformal dimensions as a function…
This paper introduces a novel variational approach for image compression motivated by recent PDE-based approaches combining edge detection and Laplacian inpainting. The essential feature is to encode the image via a sparse vector field,…
We address in this paper the issue of renormalizability for SU(2) Tensorial Group Field Theories (TGFT) with geometric Boulatov-type conditions in three dimensions. We prove that tensorial interactions up to degree 6 are just renormalizable…
Gauge theories in axial gauges are studied using Exact Renormalisation Group flows. We introduce a background field in the infrared regulator, but not in the gauge fixing, in contrast to the usual background field gauge. It is shown how…
Our aim is to find a complex continued fraction algorithm finding all the best Diophantine approximations to a complex number. Using the sequence of minimal vectors in a two dimensional lattice over Gaussian integers, we obtain an algorithm…
We extend our previous study of the vector charmonium states within a renormalization approach with boundary conditions to the full spectrum of charmonium and bottomonium. On the light of the predicted spectrum we comply to assignments…
We consider the periodic homogenisation problem for the generalised parabolic Anderson model on the two dimensional torus. We show that, for the renormalisation that respects Wick ordering, the homogenisation and renormalisation procedures…
Two Dimensional (2D) Transition Metal Dichalcogenides (TMDs) possess a large direct band gap which has been experimentally observed to shrink with increasing charge carrier density (doping). The effect has been the subject of theoretical…
We consider Thurston maps, i.e., branched covering maps $f\colon S^2\to S^2$ that are postcritically finite. In addition, we assume that $f$ is expanding in a suitable sense. It is shown that each sufficiently high iterate $F=f^n$ of $f$ is…
We present an alternative numerical reconstruction algorithm for direct tomographic reconstruction of a sample refractive indices from the measured intensities of its far-field coherent diffraction patterns. We formulate the well-known…
We study the two-loop renormalization group equation for the running gaugino mass in the supersymmetric gauge theory. We find that both in the \msbar and \drbar renormalization schemes, the well-known proportionality of the runnings of the…
Within finite temperature field theory, we show that truncated non-perturbative self-consistent Dyson resummation schemes can be renormalized with local counter-terms defined at the vacuum level. The requirements are that the underlying…
The Poincar\'e-Hopf Theorem is a conservation law for real-analytic vector fields, which are tangential to a closed surface (such as a torus or a sphere). The theorem also governs real-analytic vector fields, which are tangential to…
The paper considers the phase retrieval problem in N-dimensional complex vector spaces. It provides two sets of deterministic measurement vectors which guarantee signal recovery for all signals, excluding only a specific subspace and a…
Recently, it has been claimed that some complex networks are self-similar under a convenient renormalization procedure. We present a general method to study renormalization flows in graphs. We find that the behavior of some variables under…