Tutorial de grupo de Renormalização
Para Sandro e Ariadne estudarem (e talvez Paulo e Leonardo):
American Journal of Physics, Vol. 72, No. 2, pp. 170–184, February 2004
©2004 American Association of Physics Teachers. All rights reserved.
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A hint of renormalization
Bertrand Delamotte
Laboratoire de Physique Théorique et Hautes Energies, Universités Paris VI, Pierre et Marie Curie, Paris VII, Denis Diderot, 2 Place Jussieu, 75251 Paris Cedex 05, France
Received: 28 January 2003; accepted: 15 September 2003
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.
© 2004 American Association of Physics Teachers.
Contents
I. INTRODUCTION
II. A TOY MODEL FOR RENORMALIZATION
III. RENORMALIZABLE THEORIES WITH DIMENSIONLESS COUPLINGS
IV. RENORMALIZATION GROUP
V. SUMMARY
ACKNOWLEDGMENTS
APPENDIX A: TOY MODELS FOR RENORMALIZABLE AND NONRENORMALIZABLE PERTURBATION EXPANSIONS
APPENDIX B: DERIVATION OF EQ. (22)
APPENDIX C: LOGARITHMIC DIVERGENCES IN RENORMALIZABLE THEORIES WITH DIMENSIONLESS COUPLINGS
APPENDIX D: RENORMALIZATION GROUP IMPROVED EXPANSION
APPENDIX E: THE RENORMALIZATION GROUP APPLIED TO A DIFFERENTIAL EQUATION
REFERENCES
FIGURES
FOOTNOTES
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