Related papers: Secular Terms in Dyson Series to All-Orders of Per…
It is shown that the renormalization group method does not necessarily eliminate all secular terms in perturbation series to partial differential equations and a functional subspace of renormalizable secular solutions corresponds to a…
We revisit the issues of non-linear AdS stability, its relation to growing (secular) terms in naive perturbation theory around the AdS background, and the need and possible strategies for resumming such terms. To this end, we review a…
For singular perturbation problems in dynamical systems, various appropriate singular perturbation methods have been proposed to eliminate secular terms appearing in the naive expansion. For example, the method of multiple time scales, the…
We revisit the renormalization group (RG) theoretical perturbation theory on oscillator-type second-order ordinary differential equations. For a class of potentials, we show a simple functional relation among secular coefficients of the…
For perturbed ordinally differential equations, a procedure of renormalization group method is proposed. To uniquely obtain renormalized solutions for given initial conditions, the procedure assumes that the extra integral constants yielded…
We develop a method for treating a series of secularly growing terms obtained from quantum perturbative calculations: autonomous first-order differential equations are constructed such that they reproduce this series to the given order. The…
A natural procedure is introduced to replace the traditional, perturbatively generated counter terms to yield a formulation of covariant, self-interacting, nonrenormalizable scalar quantum field theories that has the added virtue of…
We solve the higher order equations of the theory of the strong perturbations in quantum mechanics given in M. Frasca, Phys. Rev. A 45, 43 (1992), by assuming that, at the leading order, the wave function goes adiabatically. This is…
The difficulty that the probabilities infinitely increase with time as time is long enough in time-dependent perturbation theory for some quantum systems is resolved by means of simply transforming the perturbative series into natural…
We revisit a simple toy model of two scalar fields in de Sitter space, playing the roles of "system" and "environment" degrees of freedom, which interact with each other. We show that there are secular divergences in physically relevant…
A proper formulation in the perturbative renormalization group method is presented to deduce amplitude equations. The formulation makes it possible not only avoiding a serious difficulty in the previous reduction to amplitude equations by…
We consider the classical algebra of observables that are diagonal in a given orthonormal basis, and define a complete decoherence process as a completely positive map that asymptotically converts any quantum observable into a diagonal one,…
We introduce a generalization of the conventional renormalization schemes used in dimensional regularization, which illuminates the renormalization scheme and scale ambiguities of pQCD predictions, exposes the general pattern of…
A perturbative description of Large Scale Structure is a cornerstone of our understanding of the observed distribution of matter in the universe. Renormalization is an essential and defining step to make this description physical and…
Problems of self-interaction arise in both classical and quantum field theories. To understand how such problems are to be addressed in a quantum theory of the Dirac and electromagnetic fields (quantum electrodynamics), we can start by…
We show that it is possible to extract useful information from the straightforward perturbation theory in classical mechanics. Although the secular terms make the perturbation series useless for large time, these expansions yield the…
We present evidence that decoherence can produce a smooth quantum-to-classical transition in nonlinear dynamical systems. High-resolution tracking of quantum and classical evolutions reveals differences in expectation values of…
Duality is considered for the perturbation theory by deriving, given a series solution in a small parameter, its dual series with the development parameter being the inverse of the other. A dual symmetry in perturbation theory is…
An outline is given of an extended perturbative solution of Euclidean QCD which systematically accounts for a class of nonperturbative effects, while allowing renormalization by the perturbative counterterms. Proper vertices Gamma are…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…