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We use two renormalization techniques, Effective Field Theory and the Similarity Renormalization Group, to solve simple Schr{\"o}dinger equations with delta-function potentials in one and two dimensions. The familiar one-dimensional…
The equivalence of subtractively renormalized and cut-off effective field theories is demonstrated for the example of very low energy effective field theory for the nucleon-nucleon interaction.
We review recent results in the theory of numbers and single-valued functions on the complex plane which arise in quantum field theory. We use the results to calculate the renormalization functions $\beta$, $\gamma$, $\gamma_m$ of…
The main theme of the paper is the detailed discussion of the renormalization of the quantum field theory comprising two interacting scalar fields. The potential of the model is the fourth-order homogeneous polynomial of the fields,…
These lectures review the formalism of renormalization in quantum field theories with special regard to effective quantum field theories. While renormalization theory is part of every advanced course on quantum field theory, for effective…
These are introductory lecture notes aimed at beginning graduate students covering fundamental concepts and ideas behind the renormalisation group. Our main goal is to motivate it and then explore its consequences, in the context of quantum…
Can large distance high energy QCD be described by Reggeon Field Theory as an effective emergent theory? We start to investigate the issue employing functional renormalisation group techniques.
The quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques. A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional…
Based upon the intrinsic relation between the divergent lower point functions and the convergent higher point ones in the renormalizable quantum field theories, we propose a new method for regularization and renormalization in QFT. As an…
The role of cut-off and dimensional regularizations is discussed in the context of obtaining a renormalized nucleon-nucleon potential from the chiral Lagrangian formulation of the effective field theory due to Weinberg. Both types of…
In this study, we propose a novel regularization/renormalization scheme that utilizes an auxiliary Feynman parameterization. This approach is employed to align a specified loop diagram with a designated unit of the form $1=\lambda/\lambda$.…
Current models of inter-nucleon interactions are built within the frame of Effective Field Theories (EFTs). Contrary to traditional nuclear potentials, EFT interactions require a renormalization of their parameters in order to derive…
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…
The general structure of the renormalization group equations for the low energy effective field theory formulation of pure gravity is presented. The solution of these equations takes a particular simple form if the mass scale of the…
The renormalization of higher-dimensional operators in quantum field theory is essential for phenomenological analyses in particle physics, and plays a significant role in the study of critical phenomena. We present a framework for…
The problem of renormalization of the semiclassical one-loop equations used in the non-equilibrium field theory is considered. Recently, the renormalizability of such equations has been justified for some special cases of classical field…
We investigate the renormalization of ``nonlocal" interactions which arise as an infinite sum of higher derivative interactions in an effective field theory. Using dimensional regularization with minimal subtraction in a general scalar…
Through introducing a notion of renormalization of particle-number density, a simple perturbation scheme of nonequilibrium quantum-field theory is proposed. In terms of the renormalized particle-distribution functions, which characterize…
We discuss an alternative method to mass renormalize a quantum field Hamiltonian based on a requirement that the vacuum and single-particle sectors are not self-scattering. We illustrate the feasibility of this method for the concrete…
We extend the method of differential renormalization to massive quantum field theories treating in particular $\ph4$-theory and QED. As in the massless case, the method proves to be simple and powerful, and we are able to find, in…