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Fundamental Geometric Structures for the Dirac Equation in General Relativity

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Abstract

We present an axiomatic approach to Dirac's equation in General Relativity based on intrinsically covariant geometric structures. Structure groups and the related principal bundle formulation can be recovered by studying the automorphisms of the theory. Various aspects can be most neatly understood within this context, and a number of questions can be most properly addressed (specifically in view of the formulation of QFT on a curved background). In particular, we clarify the fact that the usual spinor structure can be weakened while retaining all essential physical aspects of the theory.

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Authors and Affiliations

  1. Dipartimento di Matematica Applicata 'G. Sansone', Via S. Marta 3, 50139, Firenze, Italy

    Daniel Canarutto

  2. Institute of Theoretical Physics, pl. Maksa Borna 9, 50-204, Wrocław, Poland

    Arkadiusz Jadczyk

Authors
  1. Daniel Canarutto
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  2. Arkadiusz Jadczyk
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Canarutto, D., Jadczyk, A. Fundamental Geometric Structures for the Dirac Equation in General Relativity. Acta Applicandae Mathematicae 51, 59–92 (1998). https://doi.org/10.1023/A:1005874109388

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