How to Construct a Dirac Operator in Infinite Dimensions

2008/09/18 by Andrew Stacey, Stacey, Andrew
Mathematics · #53C15 (Secondary) #58B20 (Primary) #58D15 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C15 #msc:58B20 #msc:58D15

paper · pdf · doi:10.48550/arxiv.0809.3104

10 pages. Together with arXiv:0809.3108 this replaces math.DG/0505077

arxiv created 2008/09/18 · openalex publication_date 2008/09/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define the notion of a co-Riemannian structure and show how it can be used to define the Dirac operator on an appropriate infinite dimensional manifold. In particular, this approach works for the smooth loop space of a so-called string manifold.

Citations

• The co-Riemannian Structure of Smooth Loop Spaces

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