Related papers: A renormalization group improved non-local gravita…
The operator-theoretic renormalization group (RG) methods are powerful analytic tools to explore spectral properties of field-theoretical models such as quantum electrodynamics (QED) with non-relativistic matter. In this paper these methods…
We study the long-time asymptotics of a certain class of nonlinear diffusion equations with time-dependent diffusion coefficients which arise, for instance, in the study of transport by randomly fluctuating velocity fields. Our primary goal…
These lecture notes provide a pedagogical introduction to a specific continuum implementation of the Wilsonian renormalization group, the effective average action. Its general properties and, in particular, its functional renormalization…
A perturbative renormalization group method is used to obtain steady-state density profiles of a particle non-conserving asymmetric simple exclusion process. This method allows us to obtain a globally valid solution for the density profile…
These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general…
Using the Batalin-Vilkovisky technique and the background field method the proof of gauge invariant renormalizability is elaborated for a generic model of quantum gravity which is diffeomorphism invariant and has no other, potentially…
In this paper we employ the Renormalization Group (RG) method to study higher order corrections to the long-time asymptotics of a class of nonlinear integral equations with a generalized heat kernel and with time-dependent coefficients.…
The renormalization group method is a successive integration over the fluctuations which are ordered according to their length scale, a parameter in the external space. A different procedure is described, where the fluctuations are treated…
We derive the flow equation for the gravitational effective average action in an $f(R)$ truncation on hyperbolic spacetimes using the exponential parametrization of the metric. In contrast to previous works on compact spaces, we are able to…
We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of three dimensional (Riemannian) gravity with positive cosmological constant (Lambda>0). We show that the usual regularization techniques (successful…
The running coupling constants are introduced in Quantum Mechanics and their evolution is described by the help of the renormalization group equation. The harmonic oscillator and the propagation on curved spaces are presented as examples.…
We develop a new formalism for the treatment of gravitational backreaction in the cosmological setting. The approach is inspired by projective techniques in non-equilibrium statistical mechanics. We employ group-averaging with respect to…
Over the last several years, there has been a resurgence of interest in using non-perturbative approximation methods based on Wilson's continuous renormalization group. In this lecture, I review progress particularly in the past year,…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
These two lectures cover some of the advances that underpin recent progress in deriving continuum solutions from the exact renormalization group. We concentrate on concepts and on exact non-perturbative statements, but in the process will…
A model Hamiltonian that exhibits asymptotic freedom and a bound state, is used to show on example that similarity renormalization group procedure can be tuned to improve convergence of perturbative derivation of effective Hamiltonians,…
We present a detailed discussion of a novel dynamical renormalization group scheme: the Dynamically Driven Renormalization Group (DDRG). This is a general renormalization method developed for dynamical systems with non-equilibrium critical…
The renormalization group is used to improve the effective potential of massive ${\rm O}(N)$ symmetric $\phi^4$ theory. Explicit results are given at the two-loop level.
A new exact renormalization group equation for the effective average action of Euclidean quantum gravity is constructed. It is formulated in terms of the component fields appearing in the transverse-traceless decomposition of the metric. It…
We study the quantum gravitational system coupled to a charged scalar, Dirac fermions, and electromagnetic fields. We use the "exact" or "functional" renormalization group equation to derive the effective action $\Gamma_0$ by integrating…