Related papers: An introduction to universality and renormalizatio…
A general organizing principle is proposed that can be used to derive the equations of motion describing the near-equilibrium dynamics of causal and thermodynamically stable relativistic systems. The latter are found to display some new…
We describe new universality classes associated to generic higher character Lifshitz critical behaviors for systems with arbitrary short range competing interactions. New renormalization-group arguments are proposed for anisotropic and…
We introduce a versatile and practical framework for applying matrix product state techniques to continuous quantum systems. We divide space into multiple segments and generate continuous basis functions for the many-body state in each…
In physics one attempts to infer the rules governing a system given only the results of imperfect measurements. Hence, microscopic theories may be effectively indistinguishable experimentally. We develop an operationally motivated procedure…
Asymptotic Safety provides a mechanism for constructing a consistent and predictive quantum theory of gravity valid on all length scales. Its key ingredient is a non-Gaussian fixed point of the gravitational renormalization group flow which…
We establish the functional Renormalization Group as an exploratory tool to investigate a possible phase transition between a pre-geometric discrete phase and a geometric continuum phase in quantum gravity. In this paper, based on the…
We show how to derive fixed-point Hamiltonians in quantum mechanics from a proposed renormalization group invariance approach that relies in a subtraction procedure at a given energy scale. The scheme is valid for arbitrary interactions…
A method of quantizing parametrized systems is developed that is based on a kind of ``gauge invariant'' quantities---the so-called perennials (a perennial must also be an ``integral of motion''). The problem of time in its particular form…
Systems undergoing an equilibrium phase transition from a liquid state to an amorphous solid state exhibit certain universal characteristics. Chief among these are the fraction of particles that are randomly localized and the scaling…
We show with several examples that renormalization group (RG) theory can be used to understand singular and reductive perturbation methods in a unified fashion. Amplitude equations describing slow motion dynamics in nonequilibrium phenomena…
The Generalized Central Limit Theorem is a remarkable generalization of the Central Limit Theorem, showing that the sum of a large number of independent, identically-distributed (i.i.d) random variables with infinite variance may converge…
We review the application of field-theoretic renormalization group (RG) methods to the study of fluctuations in reaction-diffusion problems. We first investigate the physical origin of universality in these systems, before comparing RG…
The field theoretic renormalization group is applied to a simple model of random walk on a rough fluctuating surface. We consider the Fokker--Planck equation for a particle in a uniform gravitational field. The surface is modelled by the…
Recent work on the use of dimensional reduction for the regularisation of non--supersymmetric theories is reviewed. It is then shown that there exists a class of theories for which a universal form of the soft supersymmetry breaking terms…
We present a quick introduction to quantum field theory and Wilson's theory of the renormalization group from the point of view of mathematical analysis. The presentation is geared primarily towards a probability theory, harmonic analysis…
I give an overview over some work on rigorous renormalization theory based on the differential flow equations of the Wilson-Wegner renormalization group. I first consider massive Euclidean $\phi_4^4$-theory. The renormalization proofs are…
We consider self-similar solutions describing intermittent bursts in shell models of turbulence, and study their relationship with blowup phenomena in continuous hydrodynamic models. First, we show that these solutions are very close to…
We give an introduction to renormalisation, focusing first on a pedagogical description of fundamental concepts of the procedure and its features, then we introduce the renormalisation group and its equations. We discuss then the case of…
We derive quantum kinetic equations from a quantum field theory implementing a diagrammatic perturbative expansion improved by a resummation via the dynamical renormalization group. The method begins by obtaining the equation of motion of…
Application of asymptotic freedom to the ultraviolet stability in Euclidean quantum field theories is revisited and illustrated through the hierarchical model making also use of a few technical developments that followed the original works…