Related papers: A new method to solve the Non Perturbative Renorma…
Fixed-point equations in the functional renormalization group approach are integrated from large to vanishing field, where an asymptotic potential in the limit of large field is implemented as initial conditions. This approach allows us to…
In this paper, we introduce an iterative process which converges strongly to a common element of sets of solutions of finite family of generalized equilibrium problems, sets of fixed points of finite family of continuous relatively…
We combine two non-perturbative approaches, one based on the two-particle-irreducible (2PI) action, the other on the functional renormalization group (fRG), in an effort to develop new non-perturbative approximations for the field…
This paper presents a nonperturbative method for solving eigenproblems. This method applies to almost all potentials and provides nonperturbative approximations for any energy level. The method converts an eigenproblem into a perturbation…
The flow equations of the renormalisation group permit to analyse the perturbative $n$-point functions of renormalisable quantum field theories. Rigorous bounds implying renormalisablility allow to control large momentum behaviour, infrared…
Approximately 10 years ago, the method of renormalization-group symmetries entered the field of boundary value problems of classical mathematical physics, stemming from the concepts of functional self-similarity and of the Bogoliubov…
We introduce a method for reconstructing an infinitesimal normalizing flow given only an infinitesimal change to a (possibly unnormalized) probability distribution. This reverses the conventional task of normalizing flows -- rather than…
The flow equations of the Functional Renormalization Group are applied to the O(N)-symmetric scalar theory, for N=1 and N=4, in four Euclidean dimensions, d=4, to determine the effective potential and the renormalization function of the…
We summarize our renormalization group approach for the vector model as well as the matrix model which are the discretized quantum gravity in one- and two-dimensional spacetime. A difference equation is obtained which relates free energies…
We show how the exact renormalization group for the effective action with a sharp momentum cutoff, may be organised by expanding one-particle irreducible parts in terms of homogeneous functions of momenta of integer degree (Taylor…
We shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non-analytic perturbation (the latter will be assumed to have continuous derivatives up to a sufficiently large order). We shall…
A renormalization-group scheme is developed for the 3-dimensional O($2N$)-symmetric Ginzburg-Landau-Wilson model, which is consistent with the use of a 1/N expansion as a systematic method of approximation. It is motivated by an application…
Hierarchical renormalization group transformations are related to non-associative algebras. Non-trivial infrared fixed points are shown to be solutions of polynomial equations. At the example of a scalar model in $d(\ge2)$ dimensions some…
A field theoretic renormalization group method is presented which is capable of dealing with crossover problems associated with a change in the upper critical dimension. The method leads to flow functions for the parameters and coupling…
We apply the functional renormalization group method to the calculation of dynamical properties of zero-dimensional interacting quantum systems. As case studies we discuss the anharmonic oscillator and the single impurity Anderson model. We…
We show that non-perturbative fixed points of the exact renormalization group, their perturbations and corresponding massive field theories can all be determined directly in the continuum -- without using bare actions or any tuning…
We develop renormalization group methods for solving partial and stochastic differential equations on coarse meshes. Renormalization group transformations are used to calculate the precise effect of small scale dynamics on the dynamics at…
The review presents general methods for treating complicated problems that cannot be solved exactly and whose solution encounters two major difficulties. First, there are no small parameters allowing for the safe use of perturbation theory…
We present a technique for calculating non-equilibrium Green functions for impurity systems with local interactions. We use an analogy to the calculation of response functions in the x-ray problem.The initial state and the final state…
Nonlinear conservation laws subject to random initial conditions pose fundamental problems in the evolution and interactions of shocks and rarefactions. Using a discrete set of values for the solution, we derive a hierarchy of equations in…