用真空测量法检验杨米尔斯真空波函数
Testing Proposals for the Yang-Mills Vacuum Wavefunctional by Measurement of the Vacuum
摘要：
我们回顾了一种方法，多年前提出的，数值测量的相对振幅的真正的杨米尔斯真空波泛函在一组有限的晶格调控场配置。该技术适用于2+1维的阿贝尔平面波配置的变化的振幅和波长，和非阿贝尔常数配置的集合。结果进行了比较，几个建议的版本的杨-米尔斯真空波泛函，已出现在文献中的预测。这些包括（i）由于Greensite和Olejnik的时间规范的建议;（ii）Karabali，Kim和Nair提出的“新变量”波函数;（iii）结合时间规范和新变量波函数的混合建议;以及（iv）Reinhardt和同事以及Szczepaniak和同事开发的库仑规范波函数。我们发现，在大尺度上简化为“降维”形式的波泛函，即具有二维格点规范理论的概率分布形式的波泛函，当在长波长配置上进行评估时，与数据具有最佳的一致性。
英文摘要：
We review a method, suggested many years ago, to numerically measure the relative amplitudes of the true Yang-Mills vacuum wavefunctional in a finite set of lattice-regulated field configurations. The technique is applied in 2+1 dimensions to sets of abelian plane wave configurations of varying amplitude and wavelength, and sets of non-abelian constant configurations. The results are compared to the predictions of several proposed versions of the Yang-Mills vacuum wavefunctional that have appeared in the literature. These include (i) a suggestion in temporal gauge due to Greensite and Olejnik; (ii) the "new variables" wavefunction put forward by Karabali, Kim, and Nair; (iii) a hybrid proposal combining features of the temporal gauge and new variables wavefunctionals; and (iv) Coulomb gauge wavefunctionals developed by Reinhardt and co-workers, and by Szczepaniak and co-workers. We find that wavefunctionals which simplify to a "dimensional reduction" form at large scales, i.e. which have the form of a probability distribution for two-dimensional lattice gauge theory, when evaluated on long-wavelength configurations, have the optimal agreement with the data.
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