Related papers: Non-Perturbative $S$-matrix Renormalization
We demonstrate the power of a recently-proposed approximation scheme for the non-perturbative renormalization group that gives access to correlation functions over their full momentum range. We solve numerically the leading-order flow…
We consider fermion-dimer scattering in the presence of a large positive scattering length in the frame of functional renormalization group equations. A flow equation for the momentum dependent fermion-dimer scattering amplitude is derived…
We calculate the two-loop renormalization group (RG) beta-function of a massless scalar field theory from the irreducible version of Polchinski's exact RG flow equation. To obtain the correct two-loop result within this method, it is…
We develop a method to obtain the large N renormalization group flows for matrix models of 2 dimensional gravity plus branched polymers. This method gives precise results for the critical points and exponents for one matrix models. We show…
The 4PI effective action provides a a hierarchy of integral equations which have the form of Bethe-Salpeter equations. The vertex functions obtained from these equations can be used to truncate the exact renormalization group flow…
To gain a deeper understanding of the glassy phase in $p$-spin quantum models, this paper examines the dynamics of the $N$-vector $\bm{x} \in \mathbb{R}^N$ through the framework of renormalization group theory. First, we focus on…
We use the Schwinger-Dyson equations as a starting point to derive renormalization flow equations. We show that Katanin's scheme arises as a simple truncation of these equations. We then give the full renormalization group equations up to…
The G-matrix equation is most straightforwardly formulated in the resonating-group method if the quark-exchange kernel is directly used as the driving term for the infinite sum of all the ladder diagrams. The inherent energy-dependence…
This thesis presents an overview of the flow equations recently introduced by Wegner. The little known mathematical framework of the flow in the manifold of unitarily equivalent matrices, as discovered in the mathematical literature before…
We construct a novel Wetterich-type functional renormalization group equation for gravity which encodes the gravitational degrees of freedom in terms of gauge-invariant fluctuation fields. Applying a linear-geometric approximation the…
The spectral renormalization method is a powerful mathematical tool that is prominently used in spectral theory in the context of low-energy quantum field theory and its original introduction in [5, 6] constituted a milestone in the field.…
The gradient flow exponentially suppresses ultraviolet field fluctuations and removes ultraviolet divergences (up to a multiplicative fermionic wavefunction renormalization). It can be used to describe real-space Wilsonian renormalization…
A manifestly gauge invariant continuous renormalization group flow equation is constructed for pure SU(N) gauge theory. The formulation makes sense without gauge fixing and manifestly gauge invariant calculations may thus be carried out.…
We present a nonperturbative renormalization group solution of the Gell-Mann--Levy $\sigma$-model which was originally proposed as a phenomenological description of the dynamics of nucleons and mesons. In our version of the model the…
We formulate the exact Wilsonian renormalization group for a system of interacting fermions on a lattice. The flow equations for all vertices of the Wilson effective action are expressed in form of the Polchinski equation. We apply this…
We study the renormalization group flow of the average action of the stochastic Navier--Stokes equation with power-law forcing. Using Galilean invariance we introduce a non-perturbative approximation adapted to the zero frequency sector of…
We use the non-perturbative renormalization group to clarify some features of perturbation theory in thermal field theory. For the specific case of the scalar field theory with O(N) symmetry, we solve the flow equations within the local…
We study the renormalization group flow in weak power counting (WPC) renormalizable theories. The latter are theories which, after being formulated in terms of certain variables, display only a finite number of independent divergent…
We derive the Wilson-Polchinski RG equation in the planar limit. We explain that the equation necessarily involves also non-planar amplitudes with sphere topology, which represent multi-trace contributions to the effective action. The…
In order to obtain proper wave-function renormalization constants for unstable fermion and consist with Breit-Wigner formula in the resonant region, We have assumed an extension of the LSZ reduction formula for unstable fermion and adopted…