Related papers: Fifty years of Wilsonian renormalization and count…
In this introductory chapter, we outline expectations for when and how the hydrogen and helium atoms in the universe turned from neutral to ionized, focusing on the earliest, least well understood stages, and emphasizing the most important…
We review, in a historical perspective, developments in physics which led to the emergence of unifying ideas and theories. Some attention is paid to the theoretical programme that started in the second decade of the XXth century and whose…
I summarize what we know of renormalons from the 1970s and 80s: their uses and theoretical status. It is emphasized that renormalons in QCD are closely related to the Wilsonean operator product expansion (OPE) - a setup ideally suited for…
We show that the Wilsonian formulation of the renormalization group (RG) defines a quantum channel acting on the momentum-space density matrices of a quantum field theory. This information theoretical property of the RG allows us to derive…
We reformulate the problem of the "interpretation of quantum mechanics" as the problem of DERIVING the quantum mechanical formalism from a set of simple physical postulates. We suggest that the common unease with taking quantum mechanics as…
We survey the recent progress made in understanding non equilibrium dynamics in closed random systems. The emphasis is on the important role played by concepts from quantum information theory and on the application of systematic…
We introduce an approach to the foundations of physics that is more in line with the foundations of mathematics. The idea is to examine current theories and find a set of starting physical assumptions that are sufficient to rederive them,…
Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…
We investigate to what extent renormalization can be understood as an algebraic manipulation on concatenated one-loop integrals. We find that the resulting algebra indicates a useful connection to knot theory.
I review various aspects of Feynman integrals, regularization and renormalization. Following Bloch, I focus on a linear algebraic approach to the Feynman rules, and I try to bring together several renormalization methods found in the…
We review our proof that in a scaling limit, the time evolution of a quantum particle in a static random environment leads to a diffusion equation. In particular, we discuss the role of Feynman graph expansions and of renormalization.
We review the theory of renormalization, including perturbative renormalization, regularized functional integrals, Renormalization Group and rigorous renormalization.
In this article, I give a pedagogical introduction and overview of percolation theory. Special emphasis will be put on the review of some of the most prominent of the algorithms that have been devised to study percolation numerically. At…
In this work, we focus on on the approach by noncommutative formal power series to study the combinatorial aspects of the renormalization at the singularities in $\{0,1,+\infty\}$ of the solutions of nonlinear differential equations…
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is employed to address the hitherto nonrenormalizable gravitational interaction following which the…
This paper will be published in ``50 years of the renormalization group", dedicated to the memory of Michael E. Fisher, edited by Amnon Aharony, Ora Entin-Wohlman, David Huse, and Leo Radzihovsky, World Scientific. I start with a review of…
As quantum theory celebrates its 100th birthday, spectacular successes are mixed with outstanding puzzles and promises of new technologies. This article reviews both the successes of quantum theory and the ongoing debate about its…
We investigate the back reaction of cosmological perturbations on the evolution of the Universe using the renormalization group method. Starting from the second order perturbed Einstein's equation, we renormalize a scale factor of the…
Renormalization is a powerful technique in statistical physics to extract the large-scale behavior of interacting many-body models. These notes aim to give an introduction to perturbative methods that operate on the level of the stochastic…
Time-dependent renormalization was employed to derive a nonlinear quantum master equation (QME), in which the dynamics of a non-equilibrium fluctuation in an irrelevant system are fed back into that of a relevant one. In terms of…