arXiv 1809.024152018-09-07hep-lat

非阿贝尔格点场论的阿贝尔色循环和阿贝尔色通量对偶方法

Abelian color cycle and abelian color flux dualization methods for non-abelian lattice field theories

Carlotta Marchis

备注：: PhD thesis. 109 pages, 24 figures. This thesis is based on the work done during my PhD arXiv:1712.07546, arXiv:1710.08745, arXiv:1709.04691, arXiv:1611.01022 and arXiv:1609.00124

摘要：

在这篇论文中，我们介绍了\textit{abelian color cycle}（ACC）和\textit{abelian color flux}（ACF）方法在几个模型中的应用：SU（2）主手征模型，具有交错费米子的SU（2）规范理论和具有交错费米子的QCD。我们的方法的关键步骤在于将模型的动作分解为最小单元。对于规范理论，这些最小项是复数，我们称之为阿贝尔色循环，而对于费米子，作用量被分解为格拉斯曼双线性，我们称之为阿贝尔色通量。作为这些分解的结果，作用量是对易项的和，因此人们可以通过分解和扩展玻尔兹曼重量来进行理论的对偶化，就像在阿贝尔情况下一样。一旦传统场被整合出去，扩展指数（所谓的二元变量）就成为描述系统的新自由度。在常规字段上的积分导致权重因子和约束。这些约束以对偶形式实现了理论的对称性，并意味着对长程物理学有贡献的对偶组态是规范自由度的世界面和物质场的世界线。另一方面，权重因子允许将对偶配分函数组织成强耦合序列，其中所有项以封闭形式已知。此外，依赖于化学势的形式允许我们将净粒子数确定为对偶表象中世界线的总净时间缠绕数。

英文摘要：

In this thesis we present the application of the \textit{abelian color cycle} (ACC) and the \textit{abelian color flux} (ACF) methods to several models: the SU(2) principal chiral model, the SU(2) gauge theory with staggered fermions and QCD with staggered fermions. The key step of our approaches consists in decomposing the action of the model one is considering into its minimal units. For gauge theories those minimal terms are complex numbers, which we refer to as abelian color cycles, while for fermions the action is decomposed into Grassmann bilinears, which we called abelian color fluxes. As a result of these decompositions the actions are sums of commuting terms, and thus one can proceed with the dualization of the theory as in the abelian case, by factorizing and expanding the Boltzmann weight. The expansion indices, so-called dual variables, become the new degrees of freedom for the description of the system once the conventional fields are integrated out. The integration over the conventional fields results into weight factors and constraints. The constraints implement the symmetries of the theory in the dual form and imply that the dual configurations which contribute to the long range physics are worldsheets for the gauge degrees of freedom and worldlines for matter fields. On the other hand, the weight factors allow one to organize the dual partition function into a strong coupling series of which all terms are known in closed form. Moreover, the form of the dependence on the chemical potential allows one to identify the net-particle number as the total net temporal winding number of the worldlines in the dual representation.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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