Clover improvement, spectrum and Atiyah-Singer index theorem for the Dirac operator on the lattice
Clover improvement, spectrum and Atiyah-Singer index theorem for the Dirac operator on the lattice
复制标题
格上狄拉克算子的 Clover 改进、谱和 Atiyah-Singer 指数定理
DOI：
10.1016/s0550-3213(98)00826-8
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
I. Hip
中科院分区：
文献类型：
--
作者：
C. Gattringer;I. Hip
利用冷却和热化SU(2)规范场结构研究了O(a)-改进三叶草项在晶格狄拉克算子谱中的作用。对于冷却构型，我们观察到加入三叶草项对光谱性质的改善。对于没有三叶草项的热化情况（124,β = 2.4），我们发现物理分支和加倍分支的分离相当糟糕，这使得晶格上的Atiyah-Singer指标定理的概率解释对β和晶格大小有疑问。添加三叶草项会产生额外的实特征值，这些实特征值以相反的手性成对出现，从而进一步恶化了指标定理的情况。
We study the role of the O(a)-improving clover term for the spectrum of the lattice Dirac operator using cooled and thermalized SU(2) gauge field configurations. For cooled configurations we observe improvement of the spectral properties when adding the clover term. For the thermalized case (124, β = 2.4) without clover term we find a rather bad separation of physical and doubler branches making a probabilistic interpretation of the Atiyah-Singer index theorem on the lattice questionable for this β and lattice size. Adding the clover term leads to the creation of additional real eigenvalues which come in pairs of opposite chirality thus further worsening the situation for the index theorem.