标题： 谱不对称性通过伪微分投影：无质量狄拉克算子 显示英文标题

标题： Spectral asymmetry via pseudodifferential projections: the massless Dirac operator

摘要： 关于闭流形上偏微分方程（PDE）系统的谱不对称性研究提出了一种新的方法。最近，第一作者及其合作者发表了一系列论文，在这些论文中，他们展示了谱不对称性的信息可以编码在一个负阶伪微分算子——不对称算子——中，并可以从这个算子中恢复出来，该算子由适当定义的伪微分（谱）投影构造而成。 在本文档中，我们应用这些技术来研究无质量狄拉克算子；特别是，我们计算了不对称算子的主符号，解释了潜在的规范不变性。 显示英文摘要

摘要： A new approach to the study of spectral asymmetry for systems of partial differential equations (PDEs) on closed manifolds was proposed in a recent series of papers by the first author and collaborator. They showed that information on spectral asymmetry can be encoded within and recovered from a negative order pseudodifferential operator -- the asymmetry operator -- constructed from appropriately defined pseudodifferential (spectral) projections. In this manuscript we apply these techniques to the study of the massless Dirac operator; in particular, we compute the principal symbol of the asymmetry operator, accounting for the underlying gauge invariance.