相关论文: Exact renormalization groups and transportation of…

The presence of isotropic Lifshitz points for a U(1) symmetric scalar theory is investigated with the help of the Functional Renormalization Group at the conjectured lower critical dimension d=4. To this aim, a suitable truncation in the…

We study the functional renormalization group equation and its solutions of the gravity having the background matters. From the system equivalence eliminating vacuum divergence, we are confirmed to give Newton coupling. We also give the…

The symmetric decreasing rearrangement of functions on $\mathbb{R}^n$ features in several seminal inequalities, such as the P\'olya-Szeg\H{o} inequality. The latter was shown by the authors to hold for all smoothing rearrangements, a class…

We give a simple and elegant proof of the Equivalence Theorem, stating that two field theories related by nonlinear field transformations have the same S matrix. We are thus able to identify a subclass of nonrenormalizable field theories…

We show explicitly how the exact renormalization group equation of interacting vector models in the large N limit can be mapped into certain higher-spin equations of motion. The equations of motion are generalized to incorporate a…

This is a survey of our results on the relation between perturbative renormalization and motivic Galois theory. The main result is that all quantum field theories share a common universal symmetry realized as a motivic Galois group, whose…

An elementary introduction to perturbative renormalization and renormalization group is presented. No prior knowledge of field theory is necessary because we do not refer to a particular physical theory. We are thus able to disentangle what…

Let G be a free product of a finite family of finite groups, with the set of generators being formed by the union of the finite groups. We consider a transient nearest-neighbour random walk on G. We give a new proof of the fact that the…

The application of the exact renormalisation group to a many-fermion system with a short-range attractive force is studied. We assume a simple ansatz for the effective action with effective bosons, describing pairing effects and derive a…

The detection of gravitational waves has intensified the need for efficient, high-precision modeling of the two-body problem in General Relativity. Current analytical methods, primarily the Post-Minkowskian and Post-Newtonian expansions,…

An application of the exact renormalization group equations to the scalar field theory in three dimensional euclidean space is discussed. We show how to modify the original formulation by J. Polchinski in order to find the Wilson-Fisher…

A new singular perturbation method based on the Lie symmetry group is presented to a system of difference equations. This method yields consistent derivation of a renormalization group equation which gives an asymptotic solution of the…

The problem of two coupled scalar fields, one with mass much lighter than the other is analysed by means of Wilson's renormalization group approach. Coupled equations for the potential and the wave function renormalization are obtained by…

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…

The distance and divergence of the probability measures play a central role in statistics, machine learning, and many other related fields. The Wasserstein distance has received much attention in recent years because of its distinctions…

One of the main advantages of super-renormalizable higher derivative quantum gravity models is the possibility to derive exact beta functions, by making perturbative one-loop calculations. We perform such a calculation for the Newton…

New estimates of the critical exponents have been obtained from the field-theoretical renormalization group using a new method for summing divergent series. The results almost coincide with the central values obtained by Le Guillou and…

We study exact renormalization group equations in the framework of the effective average action. We present analytical approximate solutions for the scale dependence of the potential in a variety of models. These solutions display a rich…

The addition of certain nonrenormalizable terms to the usual action density of a free scalar field leads to nonrenormalizable theories whose exact euclidian and minkowskian Green's functions are less singular than those of the free theory.…

The two- and three-dimensional transverse-field Ising models with ferromagnetic exchange interactions are analyzed by means of the real-space renormalization group method. The basic strategy is a generalization of a method developed for the…