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摘要翻译：
我们提出了一个形式上精确的统计场论来描述经典流体，其成分类似于量子场论中引入的成分。我们考虑了以下基本的和相关的问题：i）如何找到确定配分函数的正确的场泛函（哈密顿量），ii)如何在场论中引入粒子不可分辨性的等价，iii)如何检验这种方法的有效性。我们可以使用一个简单的哈密顿量，在这个量中，局部泛函以场的形式换位，等价于粒子的不可分辨性。给出了该项的图解展开和重整化。这与费曼展开中的一个非标准问题相对应，需要仔细研究。然后在哈密顿量中引入了与相互作用对势相关的非局域项。结果表明，该方法与用Mayer函数展开给出的标准统计力学之间存在映射关系。我们从三个性质（化学势、所谓的接触定理和界面性质）证明了场论中关联式在非通常量上的移动。并对该理论提出了一些看法。
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英文标题：
《A formally exact field theory for classical systems at equilibrium》
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作者：
D. di Caprio, J.P. Badiali
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最新提交年份：
2008
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分类信息：
一级分类：Physics 物理学
二级分类：Soft Condensed Matter 软凝聚态物质
分类描述：Membranes, polymers, liquid crystals, glasses, colloids, granular matter
膜，聚合物，液晶，玻璃，胶体，颗粒物质
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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：
We propose a formally exact statistical field theory for describing classical fluids with ingredients similar to those introduced in quantum field theory. We consider the following essential and related problems : i) how to find the correct field functional (Hamiltonian) which determines the partition function, ii) how to introduce in a field theory the equivalent of the indiscernibility of particles, iii) how to test the validity of this approach. We can use a simple Hamiltonian in which a local functional transposes, in terms of fields, the equivalent of the indiscernibility of particles. The diagrammatic expansion and the renormalization of this term is presented. This corresponds to a non standard problem in Feynman expansion and requires a careful investigation. Then a non-local term associated with an interaction pair potential is introduced in the Hamiltonian. It has been shown that there exists a mapping between this approach and the standard statistical mechanics given in terms of Mayer function expansion. We show on three properties (the chemical potential, the so-called contact theorem and the interfacial properties) that in the field theory the correlations are shifted on non usual quantities. Some perspectives of the theory are given.
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PDF链接：
https://arxiv.org/pdf/707.3069
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