# 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} }

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.

## 119 Citations

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## References

SHOWING 1-10 OF 32 REFERENCES

RENORMALIZATION OF A MODEL QUANTUM FIELD THEORY

- Physics
- 1992

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

- Physics
- 1991

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

- Physics
- 1997

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

- Physics
- 1998

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

- Mathematics
- 1976

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

- Physics
- 1991

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

- Physics
- 1999

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

- Physics
- 2000

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…