Strong coupling and mean field methods in lattice gauge theories
Strong coupling and mean field methods in lattice gauge theories
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格子规范理论中的强耦合和平均场方法
DOI：
10.1016/0370-1573(83)90034-0
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发表时间：
1983
期刊：
影响因子：
--
通讯作者：
J. Zuber
中科院分区：
文献类型：
--
作者：
J. Drouffe;J. Zuber
如今，非阿贝尔规范理论在粒子物理学中起着主导作用。自发对称性破缺的机制使Salam和Weinberg建立了电弱相互作用的统一理论，并积极研究大统一理论。另一方面，渐近自由是当前强相互作用理论量子色动力学（QCD）的关键性质。这个只有非阿贝尔规范理论才享有的显著特性，保证了强子的基本成分——夸克和胶子——在短距离内的相互作用非常小。这就允许在这种状态下进行扰动处理。相反，该理论的长距离行为仍然更加难以捉摸。假设夸克的永久约束或强子谱的计算等问题是典型的强耦合问题，不能采用标准场论方法。1973年，当Wilson[1]（和Polyakov[1]）提出考虑晶格规范理论时，取得了重大突破。空间的离散化经过精心设计以保持规范不变性，提供了紫外线正则化，并且预计不会影响长距离行为，因为在小距离处的有效耦合非常弱。晶格规范理论可以被认为是统计力学的一个模型，因此适用于这些模型中使用的所有技术[3,1 -系列展开，平均场近似，蒙特卡罗模拟，…]。这是用an完成的
Non-Abelian gauge theories play nowadays a dominant role in particle physics. The mechanism of spontaneous symmetry breaking has enabled Salam and Weinberg to construct a unified theory of electroweak interactions, and grand unified theories are actively studied. On the other hand, asymptotic freedom is the crucial property of the current theory of strong interactions, quantum chromodynamics (QCD). This remarkable property, that only non-Abelian gauge theories enjoy, guarantees that fundamental constituents of hadrons—quarks and gluons—have vanishingly small interactions at short distances. This allows a perturbative treatment in this regime. On the contrary, the long distance behaviour of that theory remains more elusive. Such problems, as the assumed permanent confinement of quarks or the computation of hadron spectrum, are typically strong coupling problems and cannot resort to standard field theoretical methods.A major breakthrough was accomplished in 1973 when Wilson [1](and Polyakov [2]) proposed to consider lattice gauge theories. The discretization of space, carefully designed to preserve gauge invariance, offers an ultraviolet regularization and is not expected to affect the long distance behaviour, since the effective coupling at small distance is very weak. A lattice gauge theory may be considered as a model of statistical mechanics and is thus amenable to all techniques used in such models [3,~ 1—series expansions, mean field approximations, Monte-Carlo simulations,...—. This has been done with an