A Hint of renormalization

@article{Delamotte2002AHO,
  title={A Hint of renormalization},
  author={Bertrand Delamotte},
  journal={American Journal of Physics},
  year={2002},
  volume={72},
  pages={170-184}
}
  • 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. 
View PDF on arXiv
118 Citations
Highly Influential Citations
3
Background Citations
29
Methods Citations
14

Figures from this paper

118 Citations

Citation Type

Citation Type

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…
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 32 REFERENCES
RENORMALIZATION OF A MODEL QUANTUM FIELD THEORY
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…
Renormalization group and probability theory
Abstract The renormalization group has played an important role in the physics of the second half of the 20th century both as a conceptual and a calculational tool. In particular, it provided the key…
Exact renormalization group equations. An Introductory review
We critically review the use of the exact renormalization group equations (ERGE) in the framework of the scalar theory. We lay emphasis on the existence of different versions of the ERGE and on an…
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…
...
1
2
3
4
...