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Nonperturbative Renormalization Group and Bose-Einstein Condensation

  • Jean-Paul BlaizotEmail author
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 852)

Abstract

These lectures are centered around a specific problem, the effect of weak repulsive interactions on the transition temperature \(T_c\) of a Bose gas. This problem provides indeed a beautiful illustration of many of the techniques which have been discussed at this school on effective theories and renormalization group. Effective theories are used first in order to obtain a simple hamiltonian describing the atomic interactions: because the typical atomic interaction potentials are short range, and the systems that we consider are dilute, these potentials can be replaced by a contact interaction whose strength is determined by the \(s\)-wave scattering length. Effective theories are used next in order to obtain a simple formula for the shift in \(T_c\): this comes from the fact that near \(T_c\) the physics is dominated by low momentum modes whose dynamics is most economically described in terms of classical fields. The ingredients needed to calculate the shift of \(T_c\) can be obtained from this classical field theory. Finally the renormalization group is used both to obtain a qualitative understanding, and also as a non perturbative tool to evaluate quantitatively the shift in \(T_c\).

Keywords

Renormalization Group Effective Theory Classical Field Single Particle State External Momentum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

Most of the material of these lectures is drawn from work done in a most enjoyable collaboration with several people during these last years: G. Baym, F. Laloë, M. Holzmann, R. Mendez-Galain, D. Vautherin, N. Wschebor and J. Zinn-Justin. I would also like to express my gratitude to Achim Schwenk for insisting on having these lecture notes....and putting such a high cut-off on his patience as he waited for them.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institute of Theoretical Physics (IPhT)CEA SaclayGif-sur-Yvette CedexFrance

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