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摘要翻译：
这些讲座围绕着一个具体的问题，弱排斥相互作用对玻色气体转变温度T_C$的影响。这个问题确实提供了一个很好的例子，说明了许多技术，在有效理论和重整化群上，在这个学派已经讨论过。为了得到描述原子相互作用的简单哈密顿量，首先使用有效理论：由于典型的原子相互作用势是短程的，而我们所考虑的体系是稀的，这些势可以用强度由S波散射长度决定的接触相互作用来代替。接下来使用有效的理论来得到一个关于$T_C$移动的简单公式：一个利用了这样一个事实，即在$T_C$附近，物理由低动量模控制，其动力学用经典场来描述是最经济的；计算$t_c$位移所需的成分可以从这个经典场论中得到。最后，我们用重整化群来获得定性的理解，并作为一个非扰动的工具来定量地评估$T_C$中的位移。
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英文标题：
《Non Perturbative Renormalization Group and Bose-Einstein Condensation》
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作者：
Jean-Paul Blaizot
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
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 $T_c$: one exploits there 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 $T_c$.
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PDF链接：
https://arxiv.org/pdf/801.0009
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