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Clifford Bundles and Clifford Algebras

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Lectures on Clifford (Geometric) Algebras and Applications

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.

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Authors and Affiliations

  1. Department of Mathematics, The University of Iowa, 52242, Iowa City, IA, USA

    Thomas Branson

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  1. Thomas Branson
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Editors and Affiliations

  1. Department of Mathematics, Tennessee Technological University, Cookeville, TN, 38505, USA

    Rafal Abłamowicz

  2. Dept. de Física y Matemáticas, Universidad de las Américas—Puebla, Santa Catarina Mártir, Cholula, Puebla, 72820, México

    Garret Sobczyk

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Branson, T. (2004). Clifford Bundles and Clifford Algebras. In: Abłamowicz, R., Sobczyk, G. (eds) Lectures on Clifford (Geometric) Algebras and Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8190-6_6

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  • DOI: https://doi.org/10.1007/978-0-8176-8190-6_6

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-0-8176-3257-1

  • Online ISBN: 978-0-8176-8190-6

  • eBook Packages: Springer Book Archive

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