Related papers: Practical Algebraic Renormalization
We present the first numerical implementation of a non-perturbative renormalization method for lattice operators, based on the study of correlation functions in coordinate space at short Euclidean distance. The method is applied to compute…
This article aims at advancing the recently introduced exponential method for renormalisation in perturbative quantum field theory. It is shown that this new procedure provides a meaningful recursive scheme in the context of the algebraic…
We address the question of whether the quantum scale-invariant theories introduced in [1] are renormalizable or play the role of effective field theories that are valid below the Planck scale $M_P$. We show that starting from two-loop level…
An extension of the non-local regularization scheme is formulated in the Sp(2) symmetric Lagrangian BRST quantization framework. It generates a systematic treatment of the anomalous quantum master equations and allows to substract the…
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…
We introduce a numerical method to study critical properties near classical and quantum phase transitions. Our method applies ideas of the Tensor Renormalization Group to obtain an improved action which is used to extract critical…
These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general…
We consider the method of self-similar renormalization for calculating critical temperatures and critical indices. A new optimized variant of the method for an effective summation of asymptotic series is suggested and illustrated by several…
In this work, we consider the inverse problem of reconstructing the internal structure of an object from limited x-ray projections. We use a Gaussian process prior to model the target function and estimate its (hyper)parameters from…
We develop the method of the hamiltonian reduction of affine Lie superalgebras to obtain explicit and general expressions both for the classical and the quantum extended superconformal algebras. By performing the gauge transformation which…
Definition of Feynman integrals as solutions of some well defined systems of differential equations is proposed. This definition is equivalent to usual one but needs no regularization and application of $R$-operation. It is argued that…
Approximately 10 years ago, the method of renormalization-group symmetries entered the field of boundary value problems of classical mathematical physics, stemming from the concepts of functional self-similarity and of the Bogoliubov…
We consider the exact renormalization group for a non-canonical scalar field theory in which the field is coupled to the external source in a special non linear way. The Wilsonian action and the average effective action are then simply…
Quantum hamiltonian reduction is a fundamental tool of conformal field theory and vertex algebra representation theory. It has traditionally been applied to study highest-weight modules. On the other hand, inverse quantum hamiltonian…
We reexamine a unitary-transformation method of extracting a physical Hamiltonian from a gauge field theory after quantizing all degrees of freedom including redundant variables. We show that this {\it quantum Hamiltonian reduction} method…
By parametrizing the action integral for the standard Schrodinger equation we present a derivation of the recently proposed method for quantizing a parametrized theory. The reformulation suggests a natural extension from conventional to…
In this work, we focus on on the approach by noncommutative formal power series to study the combinatorial aspects of the renormalization at the singularities in $\{0,1,+\infty\}$ of the solutions of nonlinear differential equations…
We present a perturbative construction of interacting quantum field theories on any smooth globally hyperbolic manifold. We develop a purely local version of the Stueckelberg-Bogoliubov-Epstein-Glaser method of renormalization using…
This talk describes the resummation approach in (Fractional) Analytic Perturbation Theory (FAPT) in QCD. First, we make a short historical review of the (F)APT approach and then shortly describe the global scheme of FAPT which allows one to…
On the basis of a thorough discussion of the Batalin-Vilkovisky formalism for classical field theory presented in our previous publication, we construct in this paper the Batalin-Vilkovisky complex in perturbatively renormalized quantum…