Related papers: Non-linear and weak-coupling expansion in Quantum …
The problem of renormalization in perturbative quantum field theory (pQFT) can be described in a rigorous way through the theory of extension of distributions. In the framework of pQFT a certain type of distribution appears, given by…
We demonstrate the renormalisability of quantum field theories in four dimensions with elementary self-interacting Dirac fermions and to leading order in the limit of many fermion flavours $N_{\rm f}$. Starting from the underlying…
A particular choice of renormalization, within the simplifications provided by the non-perturbative property of Effective Locality, leads to a completely finite, renormalized theory of QCD, in which all correlation functions can, in…
Diagrammatic approach proposed many years ago for strong correlated Hubbard model is developed for analyzing of the thermodynamic potential properties. The new exact relation between such renormalized quantities as thermodynamic potential,…
In recent years, the investigation of nonlinear electromagnetic responses has received significant attention due to its potential for elucidating the quantum properties of matter. Although remarkable progress has been achieved in developing…
We study a self-interacting scalar field theory in the presence of a \delta-function background potential. The role of surface interactions in obtaining a renormalizable theory is stressed and demonstrated by a two-loop calculation. The…
I show that under certain conditions it is possible to define consistent irrelevant deformations of interacting conformal field theories. The deformations are finite or have a unique running scale ("quasi-finite"). They are made of an…
We review some aspects of the renormalization group method for interacting fermions. Special emphasis is placed on the application of scaling theory to quasi-one-dimensional systems at non zero temperature. We begin by introducing the…
I propose an approximation scheme for asymptotically free field theories combining both weak coupling and strong coupling series. The weak coupling expansion is used to integrate the high frequency modes and the resulting low energy…
In the spirit of classic works of Wilson on the renormalization group and operator product expansion, a new framework for the study of the theory space of euclidean quantum field theories has been introduced. This formalism is particularly…
A method to obtain all-order asymptotic results for the coefficients of perturbative expansions in zero-dimensional quantum field is described. The focus is on the enumeration of the number of skeleton or primitive diagrams of a certain QFT…
I review the theory of renormalization, as applied to weak-coupling perturbation theory in quantum field theories.
A recently-proposed technique, called the dimensional expansion, uses the space-time dimension $D$ as an expansion parameter to extract nonperturbative results in quantum field theory. Here we apply dimensional-expansion methods to examine…
Building on our recent derivation of the Ward-Schwinger-Dyson equations for the cubic interaction model, we present here the first steps of their resurgent analysis. In our derivation of the WSD equations, we made sure that they had the…
The paper is an attempt to relate two vast areas of the applicability of the renormalization group (RG): field theoretic models and partial differential equations. It is shown that the Green function of a nonlinear diffusion equation can be…
We argue that the renormalizability of interacting quantum field theory on the curved-space background with an additional external antisymmetric tensor (two-form) field requires nonminimal interaction of the antisymmetric field with quantum…
We propose a new class of single-field scalar quantum field theories with non-polynomial interactions leading to a two-point Green's function that can be naturally continued beyond the naive cutoff scale. This provides a new prospect for…
A series of informal seminars at graduate-student level on the subject of coupling dependence in quantum field theory, with an elementary introduction to the notion of resurgent function that forms the appropriate framework for the coupling…
We discuss the connection between the perturbative and non-perturbative renormalization and related conceptual issues in the few-nucleon sector of the low-energy effective field theory of the strong interactions. General arguments are…
Arguments are provided which show that extension of renormalizability in quantum field theory is possible. A dressed scheme for the perturbation expansion is proposed. It is proven that in this scheme a nonrenormalizable interaction becomes…