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Letters in Mathematical Physics

, Volume 107, Issue 5, pp 933–961 | Cite as

A universal spinor bundle and the Einstein–Dirac–Maxwell equation as a variational theory

  • Olaf Müller
  • Nikolai Nowaczyk
Article

Abstract

Not only the Dirac operator, but also the spinor bundle of a pseudo-Riemannian manifold depends on the underlying metric. This leads to technical difficulties in the study of problems where many metrics are involved, for instance in variational theory. We construct a natural finite dimensional bundle, from which all the metric spinor bundles can be recovered including their extra structure. In the Lorentzian case, we also give some applications to Einstein–Dirac–Maxwell theory as a variational theory and show how to coherently define a maximal Cauchy development for this theory.

Keywords

Spin geometry Spinor bundle Jet spaces Natural constructions Einstein–Dirac–Maxwell equation Cauchy development 

Mathematics Subject Classification

35L03 53C27 58J45 83C22 

Notes

Acknowledgements

The authors would like to thank Bernd Ammann and Felix Finster for interesting discussions and suggestions.

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität RegensburgRegensburgGermany
  2. 2.Maths DepartmentImperial CollegeLondonUnited Kingdom

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