Twistor sections of Dirac bundles
| Autor: | Sergio A. H. Cardona, Iván Téllez, Pedro Solórzano |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Mathematics - Differential Geometry
High Energy Physics - Theory Dirac (software) General Physics and Astronomy FOS: Physical sciences Clifford bundle Curvature Dirac operator 01 natural sciences Twistor theory symbols.namesake 0103 physical sciences FOS: Mathematics 0101 mathematics Metric connection Mathematical Physics Mathematical physics Mathematics 010102 general mathematics Mathematical Physics (math-ph) Riemannian manifold Differential Geometry (math.DG) High Energy Physics - Theory (hep-th) Bundle symbols 010307 mathematical physics Geometry and Topology Mathematics::Differential Geometry 53C28 (Primary) 53C27 53C07 (Secondary) |
| Popis: | A Dirac bundle is a euclidean bundle over a riemannian manifold $M$ which is a compatible left $C\ell(M)$-module, together with a metric connection also compatible with the Clifford action in a natural way. We prove some vanishing theorems and introduce the twistor equation within this framework. In particular, we exhibit a characterization of solutions for this equation in terms of the Dirac operator $D$ and a suitable Weitzenb\"ock-type curvature operator $\mathcal{R}$. Finally, we analyze the especial case of the Clifford bundle to prove existence of nontrivial solutions of the twistor equation on spheres. Comment: 24 pages, no figures |
| Databáze: | OpenAIRE |
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