标题： 量子色动力学中具有手征对称性的格点费米子的模拟 显示英文标题

标题： Simulations of Lattice Fermions with Chiral Symmetry in Quantum Chromodynamics

摘要： 本论文致力于探索QCD中用于提取物理信息的$\epsilon$区域内的数值计算可行性。我们应用两种Ginsparg-Wilson费米子的形式：Neuberger算子和超立方重叠算子来计算感兴趣的可观测量。 我们的主要结果是展示了QCD中Neuberger算子的主要单个特征值分布与手征随机矩阵理论的解析预测之间的比较。只要物理体积的每一侧超过大约$L\approx 1.12\fm$，我们就观察到良好的一致性。结果表明，对于$L$来说，这个界限是通用的，并决定了轴向关联函数根据手征微扰理论行为的物理体积大小。这使我们能够计算出π介子衰变常数$F_{\pi}$的值。 作为一种替代方法，我们只考虑零模贡献。在这里，我们能够估算$F_{\pi}$和$\alpha$。作为理论发展的一部分，研究了Lüscher拓扑守恒规范作用量。这使得我们能够在$\epsilon$区域内采样感兴趣的可观测量而无需重新计算指标。我们可以报告，已经识别出一个有前景的规范作用量。 显示英文摘要

摘要： This thesis is dedicated to explore the feasibility of numerical calculations in the $\epsilon$--regime of QCD for the extraction of physical information. We apply two formulations of the Ginsparg-Wilson fermions the Neuberger operator and the hypercube overlap operator to compute the observables of interest. As a main result we present the comparison of the distributions of the leading individual eigenvalues of the Neuberger operator in QCD and the analytical predictions of chiral random matrix theory. We observe a good agreement as long as each side of the physical volume exceeds about $L\approx 1.12\fm$. It turns out that this bound for $L$ is generic and sets the size of the physical volume where the axial correlator behaves according to chiral perturbation theory. This allows us to compute a value for the pion decay constant $F_{\pi}$. As an alternative procedure we only consider the contribution from the zero modes. Here we are able to obtain an estimate for $F_{\pi}$ and $\alpha$. As a theoretical development the L\"uscher topology conserving gauge action is investigated. This enables us to sample the observables of interest in the $\epsilon$--regime without recomputing the index. We can report that a promising gauge action has been identified.