Related papers: Systematic Resummed Perturbation Theory
This article aims to explain essential elements of perturbation theory and their conceptual underpinnings. It is not meant as a summary of popular perturbation methods, though some illustrative examples are given to underline the main…
Using the basic ingredient of supersymmetry, we develop a simple alternative approach to perturbation theory in one-dimensional non-relativistic quantum mechanics. The formulae for the energy shifts and wave functions do not involve tedious…
A formalism is presented to obtain closed evolution equations for asymptotic probability distribution functions of turbulence magnitudes. The formalism is derived for a generic evolution equation, so that the final result can be easily…
Based on a previously developed recursive approach for calculating the short-time expansion of the propagator for systems with time-independent potentials and its time-dependent generalization for simple single-particle systems, in this…
Starting from a hyperbolic toral automorphism, we obtain, for a small volume preserving perturbation, an exact and rigorous second order perturbation expansion of the Lyapunov exponents.
Regular sequences are natural generalisations of fixed points of constant-length substitutions on finite alphabets, that is, of automatic sequences. Using the harmonic analysis of measures associated with substitutions as motivation, we…
We provide a systematic formula, in terms of integer partitions, that generates perturbation theory explicitly at an arbitrary order. Our approach naturally includes an infinite number of perturbations and uses a single matrix equation that…
The symmetry analysis of Ermakov systems is extended to the generalized case where the frequency depends on the dynamical variables besides time. In this extended framework, a whole class of nonlinearly coupled oscillators are viewed as…
For nonlinear wave equations with a potential term we prove pointwise space-time decay estimates and develop a perturbation theory for small initial data. We show that the perturbation series has a positive convergence radius by a method…
It is shown how a recent method to systematically extrapolate and resum the loop expansion for nonlinear sigma-models is related to solutions of the renormalization group equation. This relation is used to generalize the explicit equations…
We derive an off-shell recursion relation for correlators that holds at all loop orders. This allows us to prove how generalized amplitudes transform under generic field redefinitions, starting from an assumed behavior of the…
An extended formulation of a polytope is a linear description of this polytope using extra variables besides the variables in which the polytope is defined. The interest of extended formulations is due to the fact that many interesting…
We develop a framework for Large Scale Structure (LSS) perturbation theory, that solves the Vlasov-Poisson system of equations for the distribution function in full phase space. This approach relaxes the usual apriori assumption of…
We demonstrate that the large-N expansion of Wilson loop expectation values in SO(N) and Sp(N) Yang-Mills theory on orientable and nonorientable surfaces has a natural description as a weighted sum over covers of the given surface. The sum…
We formulate a method of performing non-perturbative calculations in quantum field theory, based upon a derivative expansion of the exact renormalization group. We then proceed to apply this method to the calculation of critical exponents…
Propagators of unstable particles are considered in the spectral representation which naturally follows from the concept of continuous mass. The spectral functions are found with the help of the most general formal and physical assumptions.…
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…
We propose a new generalized version of the QCD Analytic Perturbation Theory of Shirkov and Solovtsov for the computation of higher-order corrections in inclusive and exclusive processes. We construct non-power series expansions for the…
We introduce the notion of an approximation system as a generalization of Taylor approximation, and we give some first examples. Next we develop the general theory, including error bounds and a sufficient criterion for convergence. More…
A novel method of summation for power series is developed. The method is based on the self-similar approximation theory. The trick employed is in transforming, first, a series expansion into a product expansion and in applying the…