The spectral localizer for semifinite spectral triples

Real dimensional spaces in noncommutative geometry

In this paper we will extend the product of spectral triples to a product of semifinite spectral triples. We will prove that finite summability and regularity are preserved under taking products. Connes and Marcolli constructed for each $z\in(0,\infty)$ a type ${\rm II}_\infty$-semifinite spectral triple which can be considered as a geometric space of dimension $z$. A small adaption of their construction yields a type ${\rm I}$-semifinite spectral triple. We will investigate the properties of these semifinite spectral triples. At the same time we will also avoid the need for an infra-red cutof…

连通空间上一个新的谱三元组

A new spectral triple over a space of connections

给出了完整环代数上半有限谱三元组的一种新构造。该结构与量子引力正则相关，并且是hep-th/08021784中提出的光谱三元组的替代版本。

Callias-type operators associated to spectral triples

Callias-type (or Dirac-Schrödinger) operators associated to abstract semifinite spectral triples are introduced and their indices are computed in terms of an associated index pairing derived from the spectral triple. The result is then interpreted as an index theorem for a non-commutative analogue of spectral flow. Both even and odd spectral triples are considered, and both commutative and non-commutative examples are given.

量子引力II中的谱三元组

On Spectral Triples in Quantum Gravity II

构造了与正则量子引力正则相关的代数的半有限谱三元组。该代数由三角剖分及其重心剖分中的基环生成。底层空间可以看作是圈量子引力的无约束状态空间的规范固定。本文是关于这一主题的两篇论文中的第二篇。