Related papers: Asymptotic regularization method. A constructive a…
Application of asymptotic freedom to the ultraviolet stability in Euclidean quantum field theories is revisited and illustrated through the hierarchical model making also use of a few technical developments that followed the original works…
A renormalization group method with the Lie symmetry is presented for the singular perturbation problems. Asymptotic solutions are obtained as group-invariant solutions under approximate Lie group admitted by perturbed differential…
This work introduces topological regularization as a framework for handling ultraviolet divergences in quantum field theory, reinterpreting infinities as topological obstructions at spacetime boundaries. Through geometric compactification…
The problem of UV divergences in QFT has long been a fundamental challenge. Standard regularization techniques modify high-energy behavior to ensure well-defined integrals. However, these approaches often introduce unphysical parameters,…
Inspired by the method of smoothed asymptotics developed by Terence Tao, we introduce a new ultra-violet regularisation scheme for loop integrals in quantum field theory which we call $\eta$ regularisation. This allows us to reveal a…
The results of the mathematical theory of asymptotic operation developed in hep-th/9612037 are applied to problems of immediate physical interest. First, the problem of UV renormalizationis analyzed from the viewpoint of asymptotic…
There exist certain intrinsic relations between the ultraviolet divergent graphs and the convergent ones at the same loop order in renormalizable quantum field theories. Whereupon we may establish a new method, the intrinsic regularization…
I present a novel Four-Dimensional Regularization/Renormalization approach (FDR) to ultraviolet divergences in field theories which can be interpreted as a natural separation between physical and non physical degrees of freedom. Based on…
In the asymptotic safety paradigm, a quantum field theory reaches a regime with quantum scale invariance in the ultraviolet, which is described by an interacting fixed point of the Renormalization Group. Compelling hints for the viability…
We introduce a concept of asymptotic principal values which enables us to handle rigorously singular integrals of higher-order poles encountered in the computation of various quantities based on correlation functions of a vacuum. Several…
Through defining irreducible loop integrals (ILIs), a set of consistency conditions for the regularized (quadratically and logarithmically) divergent ILIs are obtained to maintain the generalized Ward identities of gauge invariance in…
We use functional renormalization group methods to study gravity minimally coupled to a free scalar field. This setup provides the prototype of a gravitational theory which is perturbatively non-renormalizable at one-loop level, but may…
We show with several examples that renormalization group (RG) theory can be used to understand singular and reductive perturbation methods in a unified fashion. Amplitude equations describing slow motion dynamics in nonequilibrium phenomena…
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…
A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects. The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from…
In view of various field-theoretic reasons, in the present work, we study the question of if the usual dimensional regularization can be extended to quantum field theories with an ultraviolet cutoff (Poincare-breaking scale) in a way…
The structure of the UV divergencies in higher dimensional nonrenormalizable theories is analysed. Based on renormalization operation and renormalization group theory it is shown that even in this case the leading divergencies (asymptotics)…
The perturbative renormalization group(RG) equation is applied to resum divergent series of perturbative wave functions of quantum anharmonic oscillator. It is found that the resummed series gives the cumulant of the naive perturbation…
There exist certain intrinsic relations between the ultraviolet divergent graphs and the convergent ones at the same loop order in renormalizable quantum field theories. Whereupon we present a new method, the inserter regularization method,…
To understand better the quantum structure of field theory and standard model in particle physics, it is necessary to investigate carefully the divergence structure in quantum field theories (QFTs) and work out a consistent framework to…