A Hint of renormalization

  title={A Hint of renormalization},
  author={Bertrand Delamotte},
  journal={American Journal of Physics},
  • B. Delamotte
  • Published 4 December 2002
  • Physics
  • American Journal of Physics
An elementary introduction to perturbative renormalization and renormalization group is presented. No prior knowledge of field theory is necessary because we do not refer to a particular physical theory. We are thus able to disentangle what is specific to field theory and what is intrinsic to renormalization. We link the general arguments and results to real phenomena encountered in particle physics and statistical mechanics. 

Figures from this paper

An Introduction to the Nonperturbative Renormalization Group

We give in these notes a short presentation of both the main ideas underlying Wilson’s renormalization group (RG) and their concrete implementation under the form of what is now called the

Comparison of mass renormalization schemes for simple model systems

We discuss an alternative method to mass renormalize a quantum field Hamiltonian based on the requirement that the vacuum and single-particle sectors are not self-scattering. We illustrate the

Renormalization of the classical masslessscalar field theory with quartic self-interaction

The classical theory of the massless scalar field with negative quartic selfinteraction shows asymptotic freedom and confinement. These findings might help in understanding evidence, gathered from

Exponential Renormalization

Moving beyond the classical additive and multiplicative approaches, we present an “exponential” method for perturbative renormalization. Using Dyson’s identity for Green’s functions as well as the

Renormalization without infinities – an elementary tutorial

Renormalization is an indispensable tool for modern theoretical physics. At the same time, it is one of the least appealing techniques, especially in cases where naive formulations result in

Rota-Baxter Algebras in Renormalization of Perturbative Quantum Field Theory

Recently, the theory of renormalization in perturbative quan- tum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf

Regularization, renormalization, and dimensional analysis: Dimensional regularization meets freshman E&M

We illustrate the dimensional regularization technique using a simple example from electrostatics. This example illustrates the virtues of dimensional regularization without the complications of a

Analyzing jump phenomena and stability in nonlinear oscillators using renormalization group arguments

We study the stability of a damped Duffing oscillator by employing a renormalization group method for solving nonlinear differential equations. This approach is direct and makes the study of the

Hopf algebra approach to Feynman diagram calculations

The Hopf algebra structure underlying Feynman diagrams which governs the process of renormalization in perturbative quantum field theory is reviewed. Recent progress is briefly summarized with an

Hopf algebra approach to Feynman diagram calculations

The Hopf algebra structure underlying Feynman diagrams which governs the process of renormalization in perturbative quantum field theory is reviewed. Recent progress is briefly summarized with an


Renormalization is the technique used to eliminate infinities that arise in quantum field theory. This paper shows how to renormalize a particularly simple model, in which a single mass counterterm

An analytical example of renormalization in two‐dimensional quantum mechanics

As a concrete example of the idea of renormalization, quantum mechanical scattering of particles by a two‐dimensional delta‐function potential is considered. The renormalization of the scattering

Renormalization in non-relativistic quantum mechanics

The importance and usefulness of renormalization are emphasized in non-relativistic quantum mechanics. The momentum space treatment of both two-body bound state and scattering problems involving some

Regularization and renormalization in scattering from Dirac delta potentials

Various regularization schemes used in quantum field theory, including the widely used dimensional regularization scheme, and the concept of renormalization, are introduced through the study of

How to deal with infinite integrals in quantum field theory

Infinite integrals arising in perturbative expansions to quantum field theory have to be defined by means of a regularization procedure before they can be cancelled by a renormalization of the

Quantum and statistical field theory

Part I: Critical Phenomena Introduction to critical phenomena Landau theory The Renormalization group Two-dimensional models Part II: Perturbation theory and renormalization: The Euclidean Scalar

Functional self-similarity and renormalization group symmetry in mathematical physics

The results from developing and applying the notions of functional self-similarity and the Bogoliubov renormalization group to boundary-value problems in mathematical physics during the last decade

Regularization methods for delta-function potential in two-dimensional quantum mechanics

The quantum mechanics of a bound particle in the delta-function potential in two dimensions is studied with a discussion of its regularization and renormalization. A simple regularization approach is