Related papers: An Introduction to the Nonperturbative Renormaliza…
This is a very brief introduction to Wilson's Renormalization Group with emphasis on mathematical developments.
We start a systematic analysis of supersymmetric field theories in six dimensions. We find necessary conditions for the existence of non-trivial interacting fixed points. String theory provides us with examples of such theories. We…
Basic elements of the exact renormalization group method and recent results within this approach are reviewed. Topics covered are the derivation of equations for the effective action and relations between them, derivative expansion,…
Based on the Renormalization Group method, a reduction of non integrable multi-dimensional hamiltonian systems has been performed. The evolution equations for the slowly varying part of the angle-averaged phase space density, and for the…
This paper argues that the ideas underlying the renormalization group technique used to characterize phase transitions in condensed matter systems could be useful for distinguishing computational complexity classes. The paper presents a…
In these lectures we introduce the functional renormalization group out of equilibrium. While in thermal equilibrium typically a Euclidean formulation is adequate, nonequilibrium properties require real-time descriptions. For quantum…
After a brief presentation of the exact renormalization group equation, we illustrate how the field theoretical (perturbative) approach to critical phenomena takes place in the more general Wilson (nonperturbative) approach. Notions such as…
General aspects of fundamental physics are considered. We comment the Wigner's logical scheme and modify it to adjust to modern theoretical physics. Then, we discuss the role and indicate the place of renormalization group in the logic of…
We analyze the dynamical chiral symmetry breaking in gauge theories solely by the non-perturbative renormalization group, without recourse to the Schwinger-Dyson method. First, we briefly review the basic notions and formulation, and…
These lectures are centered around a specific problem, the effect of weak repulsive interactions on the transition temperature $T_c$ of a Bose gas. This problem provides indeed a beautiful illustration of many of the techniques which have…
We introduce the general formulation of a renormalization method suitable to study the critical properties of non-equilibrium systems with steady-states: the Dynamically Driven Renormalization Group. We renormalize the time evolution…
A class of exact infinitesimal renormalization group transformations is proposed and studied. These transformations are pure changes of variables (i.e., no integration or elimination of some degrees of freedom is required) such that a…
Concerning renormalisation group theory applied to phase transitions, we examine the value of positive numerical and analytical evidence, the divergent short-wavelength behaviour of classical free fields and the absence of UV-divergences in…
The possibility that non-supersymmetric quiver theories may have a renormalization-group fixed point at which there is conformal invariance requires non-perturbative information.
The non-perturbative renormalization-group approach is extended to lattice models, considering as an example a $\phi^4$ theory defined on a $d$-dimensional hypercubic lattice. Within a simple approximation for the effective action, we solve…
The running of the non-minimal parameter (\xi) of the interaction of the real scalar field and scalar curvature is explored within the non-perturbative setting of the functional renormalization group (RG). We establish the RG flow in curved…
The renormalization-group method is used to analyze the low-temperature behaviour of a two-dimentional, spin-$s$ quantum Heisenberg ferromagnet. A set of recursion equations is derived in an one-loop approximation. The low-temperature…
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…
We apply the renormalization group theory to the dynamical systems with the simplest example of basic biological motifs. This includes the interpretation of complex networks as the perturbation to simple network. This is the first step to…
We describe the Density Matrix Renormalization Group algorithms for time dependent and time independent Hamiltonians. This paper is a brief but comprehensive introduction to the subject for anyone willing to enter in the field or write the…