Related papers: Analytical continuation and resummed perturbation …
The perturbative theory of the nucleation kinetics is analyzed. A new improvement is suggested and compared with numerical calculations.
A review article on perturbation theory
The perturbation theory for critical points of causal variational principles is developed. We first analyze the class of perturbations obtained by multiplying the universal measure by a weight function and taking the push-forward under a…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Summer term 2001, to undergraduate Mathematics and Physics students. It covers a few selected topics from perturbation theory at an introductory…
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…
A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely…
The physical aspect of a general perturbation theory is explored. Its role as a physical principle for understanding the interaction among matter with different levels of hierarchy is appreciated. It is shown that the generic perturbation…
Analytic continuation of the perturbative series from spacelike to timelike regions is performed using renormalization group summed perturbation theory (RGSPT). This method provides an all-order summation of kinematic ``$\pi^2$-terms''…
Analytic structure in the strong coupling constant that emerges for some observables in QCD after duality averaging of renormalization group improved amplitudes is discussed. It is shown that perturbation theory calculations are justified…
The KAM iterative scheme turns out to be effective in many problems arising in perturbation theory. I propose an abstract version of the KAM theorem to gather these different results.
We review the construction of models of algebraic quantum field theory by renormalized perturbation theory.
Some open questions exist with fluctuation-induced forces between extended dipoles. Conventional intuition derives from large-separation perturbative approximations to dispersion force theory. Here we present a full non-perturbative theory.…
Explaining predictions based on multivariate time series data carries the additional difficulty of handling not only multiple features, but also time dependencies. It matters not only what happened, but also when, and the same feature could…
We describe the development of Analytic Perturbation Theory (APT) in QCD, called Fractional APT (FAPT), which has been suggested to apply the renormalization group evolution and QCD factorization technique in the framework of APT.
A fractal function is a function whose graph is the attractor of an iterated function system. This paper generalizes analytic continuation of an analytic function to continuation of a fractal function.
The mathematical idea of resurgence allows one to obtain nonperturbative information from the large-order behavior of perturbative expansions. This idea can be very fruitful in physics applications, in particular if one does not have access…
A method for the resummation of nonalternating divergent perturbation series is described. The procedure constitutes a generalization of the Borel-Pad\'{e} method. Of crucial importance is a special integration contour in the complex plane.…
After revealing difficulties of the standard time-dependent perturbation theory in quantum mechanics mainly from the viewpoint of practical calculation, we propose a new quasi-canonical perturbation theory. In the new theory, the dynamics…
Using resummation in perturbation theories at finite temperature or in non-equilibrium is unavoidable to obtain consistent results. Resummation, however, is often in conflict with renormalization. In this talk we give two possible solutions…