冈萨雷斯-阿罗约和基什内尔最近提出利用狄拉克算符的伴随（准）零模来探测杨-米尔斯真空。该结构依赖于超对称零模的使用，对于经典配置，它提供了规范作用密度的直接估计。在晶格实现这一想法，我们展示了如何大大改善的结果，如果重叠算子，而不是威尔逊-狄拉克之一。在详细研究蒙特卡罗系综之前，我们在这里研究了一系列可能遇到的潜在复杂情况。特别是，我们研究的情况下，瞬子反瞬子对和分析的结果如何依赖于分离。晶格伪影的影响也值得关注。事实上，在β =2.57时，热化SU（2）组态零模的统计分析显示，有相当一部分具有4 N +2个伴随零模，这与指数定理相矛盾。这种违反必须与晶格结构的粗糙度有关。事实上，我们表明，这种情况发生的瞬间的大小的顺序的晶格间距。
英文摘要：
The use of adjoint (quasi) zero-modes of the Dirac operator to probe the Yangs-Mills vacuum has been recently advocated by Gonzalez-Arroyo and Kirchner. The construction relies on the use of the super-symmetric zero mode which, for classical configurations, provides a direct estimate of the gauge action density. In the lattice implementation of this idea, we show how the results improve considerably if the overlap operator is used instead of the Wilson-Dirac one. Before proceeding to the detailed study of Monte Carlo ensembles, we studied here a series of potentially complicated situations which can be encountered. In particular, we study the case of instanton anti-instanton pairs and analyse how the results depend upon separation. The effect of lattice artifacts is also of concern. Indeed, a statistical analysis of zero modes of thermalised SU(2) configurations at beta=2.57 shows a significant fraction having 4N+2 adjoint zero modes, in contradiction with the index theorem. This violation must be associated to the roughness of the lattice configurations. Indeed, we show that this situation occurs for instantons of size of the order of the lattice spacing.
