Related papers: Perturbation theory of dynamical systems
In Causal Perturbation Theory the process of renormalization is precisely equivalent to the extension of time ordered distributions to coincident points. This is achieved by a modified Taylor subtraction on the corresponding test functions.…
An overview is given of Chiral Perturbation Theory and various applications to eta decays. In particular, the main decay $\eta\to3\pi$ is discussed at the one-loop level, and estimates of the higher order corrections are given. The…
Infrared divergences in the perturbative expansion of gauge theory amplitudes and cross sections have been a focus of theoretical investigations for almost a century. New insights still continue to emerge, as higher perturbative orders are…
We present a singular perturbation theory applicable to systems with hybrid boundary layer systems and hybrid reduced systems {with} jumps from the boundary layer manifold. First, we prove practical attractivity of an adequate attractor set…
This work assembles some basic theoretical elements on thermal equilibrium, stability conditions, and fluctuation theory in self-gravitating systems illustrated with a few examples. Thermodynamics deals with states that have settled down…
We give a short introduction for elementary mathematical tools used in the context of Quantum Field Theory. These notes were motivated by a reading group in Lyon on Talagrand's book {\guillemotleft}What is Quantum Field Theory, A First…
In these lectures we review the basic ideas of perturbative and non-perturbative string theory. On the non-perturbative side we give an introduction to D-branes and string duality. The elementary concepts of non-BPS branes and…
This article is a draft of a book chapter of the book entitled "Quantum Percolation and Breakdown", to appear 2008.
The perturbation theory with a variational basis is constructed and analyzed.The generalized Gaussian effective potential is introduced and evaluated up to the second order for selfinteracting scalar fields in one and two spatial…
This is a brief introduction to the statistical theory of fluid turbulence, with an emphasis on the field-theoretic treatment of renormalized viscosity and energy fluxes.
Cosmological perturbation theory is crucial for our understanding of the universe. The linear theory has been well understood for some time, however developing and applying the theory beyond linear order is currently at the forefront of…
This paper formulates a new approach to the study of chaos in discrete dynamical systems based on the notions of inverse ill-posed problems, set-valued mappings, generalized and multivalued inverses, graphical convergence of a net of…
The following is the very first set of the series in 'Problems and Solutions in a Graduate Course in Classical Electrodynamics'. In each of the sets of the problems we intend to follow a theme, which not only makes it unique but also deals…
A review of chiral perturbation theory and that of recent developments on the comparison of its predictions with experiment is presented. Some interesting topics with scope for further elaboration are touched upon.
Based on the gauge invariant variables proposed in our previous paper [K. Nakamura, Prog. Theor. Phys. vol.110 (2003), 723.], some formulae of the perturbative curvatures of each order are derived. We follow the general framework of the…
New models of Turbulence, Superfluidity and Superconductivity, based on new Hierarchic theory, general for liquids and solids (physics/0102086), have been proposed. CONTENTS: 1 Turbulence. General description; 2 Mesoscopic mechanism of…
In this review I discuss some basic aspects of non-perturbative string theory. The topics include test of duality symmetries based on the analysis of the low energy effective action and the spectrum of BPS states, relationship between…
The aim of these lecture notes is to familiarize graduate students and beginning postgraduates with the basic ideas of linear cosmological perturbation theory and of structure formation scenarios. We present both the Newtonian and the…
This document is an introduction to and review of two-dimensional mathematical physics. The reader is introduced to the subject matter primarily through problems, which are presented along with detailed worked solutions. For each chapter,…
A periodic perturbation generates a complicated dynamics close to separatrices and saddle points. We construct an asymptotic solution which is close to the separatrix for the unperturbed Duffing's oscillator over a long time. This solution…