Related papers: A topological approach to renormalization and its …
We give a systematic description of a canonical renormalisation procedure of stochastic PDEs containing nonlinearities involving generalised functions. This theory is based on the construction of a new class of regularity structures which…
We gain tight rigorous bounds on the renormalisation fixed point function for period doubling in families of unimodal maps with degree 2 critical point. By writing the relevant eigenproblems in a modified nonlinear form, we use these…
Electron tomography is becoming an increasingly important tool in materials science for studying the three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is…
Known results on two-dimensional quantum electrodynamics (QED_2) have been used to study the dependence of functional renormalization group equations on renormalization schemes and approximations applied for its bosonized version. It is…
We review current progress in the functional renormalization group treatment of disordered systems. After an elementary introduction into the phenomenology, we show why in the context of disordered systems a functional renormalization group…
X-ray computed tomographic infrastructures are medical imaging modalities that rely on the acquisition of rays crossing examined objects while measuring their intensity decrease. Physical measurements are post-processed by mathematical…
The renormalization-group improved effective potential ---to leading-log and in the linear curvature approximation--- is constructed for ``finite'' theories in curved spacetime. It is not trivial and displays a quite interesting,…
A tentative proposal is demonstrated that there is a natural strategy to get rid of unphysical (UV) infinities in QFTs if one adopts the modern standard point of view that a fundamental theory that is complete and well-defined in all…
Working with scalar field theories, we discuss choices of regulator that, inserted in the functional renormalization group equation, reproduce the results of dimensional regularization at one and two loops. The resulting flow equations can…
We consider scalar field theory in the D-dimensional space with nontrivial metric and local action functional of most general form. It is possible to construct for this model a generalization of renormalization procedure and RG-equations.…
A new operator formalism for the reduction of degrees of freedom in the evolution of discrete partial differential equations (PDE) via real space Renormalization Group is introduced, in which cell-overlapping is the key concept.…
Different notions on regularity of sets and of collection of sets play an important role in the analysis of the convergence of projection algorithms in nonconvex scenarios. While some projection algorithms can be applied to feasibility…
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…
INTRODUCTION This papers deals with partial differential equations of second order, linear, with constant and not constant coefficients, in two variables, which admit real characteristics. I face the study of PDEs with the mentality of the…
The main difficulty of quantum field theory is the problem of divergences and renormalization. However, realistic models of quantum field theory are renormalized within the perturbative framework only. It is important to investigate…
Using quantum electrodynamics as an example, a dependence of physical predictions of quantum field theory in a finite perturbation theory order on the choice of renormalization scheme is studied. It is shown that On-Mass-Shell…
The interest in the topological properties of materials brings into question the problem of topological phase transitions. As a control parameter is varied, one may drive a system through phases with different topological properties. What…
We study reductions of 6d theories on a $d$-dimensional manifold $M_d$, focusing on the interplay between symmetries, anomalies, and dynamics of the resulting $(6-d)$-dimensional theory $T[M_d]$. We refine and generalize the notion of…
We show that in any Euclidean space, an arbitrary probability measure can be reconstructed explicitly by its geometric (or spatial) distribution function. The reconstruction takes the form of a (potentially fractional) linear PDE, where the…
We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical…