Related papers: Perturbation theory for nonlinear equations
An explicit perturbative solution to all orders is given for a general class of nonlinear differential equations. This solution is written as a sum indexed by rooted trees and uses the Green function of a linearization of the equations. The…
Perturbation theory for a class of topological field theories containing antisymmetric tensor fields is considered. These models are characterized by a supersymmetric structure which allows to establish their perturbative finiteness.
Review of the papers on the new method of the Yang-Mills field quantization applicable both in perturbation theory and beyond it is presented. It is shown that in the modified formulation of the Yang-Mills theory leading to the formal…
The fields nonlinear modes quantization scheme is discussed. New form of the perturbation theory achieved by unitary mapping the quantum dynamics in the space $W_G$ of (action, angle)-type collective variables. It is shown why the…
Perturbative Symmetry Approach is formulated in symbolic representation. Easily verifiable integrability conditions of a given equation are constructed in the frame of the approach. Generalisation for the case of non-local and non-evolution…
A solution of the Einstein vacuum field equations is constructed within the contex of perturbation theory. The solution possesses a graphical representation in terms of diagrams.
By using a perturbation technique in critical point theory, we prove the existence of solutions for two types of nonlinear equations involving fractional differential operators.
Solutions of classical and quantum equations of motion in spinor electrodynamics are constructed within the context of perturbation theory. The solutions possess a graphical representation in terms of diagrams.
We address the problem of constructing a non-equilibrium stationary state for a one-dimensional stochastic Klein-Gordon wave equation with non-linearity, using perturbation theory. The linear theory is reviewed, but with the linear…
The difficulties of perturbation theory associated with unstable fundamental fields (such as the lack of exact gauge invariance in each order) are cured if one constructs perturbative expansion directly for probabilities interpreted as…
In this letter, we present a formal solution to the non-linear field equations of ten-dimensional super Yang--Mills theory. It is assembled from products of linearized superfields which have been introduced as multiparticle superfields in…
A perturbative formulation of algebraic field theory is presented, both for the classical and for the quantum case, and it is shown that the relation between them may be understood in terms of deformation quantization.
A general algorithm is presented which gives a closed-form expression for an arbitrary perturbative diagram of cubic string field theory at any loop order. For any diagram, the resulting expression is given by an integral of a function of…
In this paper we show how Feynman diagrams, which are used as a tool to implement perturbation theory in quantum field theory, can be very useful also in classical mechanics, provided we introduce also at the classical level concepts like…
{\it Perturbiner}, that is, the solution of field equations which is a generating function for tree form-factors in N=3 $(N=4)$ supersymmetric Yang-Mills theory, is studied in the framework of twistor formulation of the N=3 superfield…
Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our…
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…
In the present paper it is shown that the Yang-Mills equation can be represented as the equation of the non-linear electromagnetic waves superposition. The research of the topological characteristics of this representation allows us to…
By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…
We consider the general framework of perturbative quantum field theory for the general Yang-Mills model including massless and massive vector fields and also scalar and Dirac fields. We describe the chronological products using Wick…