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Recolector de Ciencia Abierta, RECOLECTA
Bachelor thesis . 2020
License: CC BY NC SA
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Dirac Operators

Authors: Mojón Álvarez, Diego;

Dirac Operators

Abstract

[EN] This work is a mostly self-contained survey on Dirac operators. It starts by laying the fundamental building blocks at the heart of spin geometry, specifically its elemental geometrical and algebraic aspects. Thus, the concepts of vector and principal bundles over manifolds, Clifford algebras, the Pin and Spin groups, the spin representation and the spinor bundle are explored. A brief commentary on connections and linear differential operators on manifolds is also provided. Subsequently, the fundamental Dirac operator is presented, along with a review of its most important basic properties. The last section is devoted to a study of the Dirac spectrum on compact manifolds, including some explicit computations and bounds of the lower nonzero eigenvalue.

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Spain
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green