Clifford Bundles and Clifford Algebras

Thomas Branson ()
Additional contact information
Thomas Branson: The University of Iowa, Department of Mathematics

Chapter 6 in Lectures on Clifford (Geometric) Algebras and Applications, 2004, pp 157-188 from Springer

Abstract: Abstract In view of General Relativity, it is necessary to study physical fields, including solutions of the Dirac equation, in curved spacetimes. It is generally believed that the study of Riemannian (positive definite) metrics (infinitesimal distance functions) will ultimately be relevant to the more directly physical problem of Lorentz signature metrics, via principles of analytic continuation in signature. This adds impetus to the natural mathematical pursuit of studying spin structure, the Dirac operator, and other related operators on Riemannian manifolds. This lecture is a biased attempt at an introduction to this subject, with an emphasis on fundamental ideas likely to be important in future work, for example, Stein-Weiss gradients, Bochner-Weitzenböck formulas, the Hijazi inequality, and the Penrose local twistor idea. This provides at least a framework for the study of advanced topics such as spectral invariants and conformal anomalies, which are not treated here.

Keywords: 53C27; 53A30; Spinor; Dirac operator; Bochner-Weitzenböck formula; Hijazi inequality; local twistors; spannors; plyors; tractors; Stein-Weiss gradients (search for similar items in EconPapers)
Date: 2004
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-8190-6_6

Ordering information: This item can be ordered from
http://www.springer.com/9780817681906

DOI: 10.1007/978-0-8176-8190-6_6

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().