Doppler shift in semi-Riemannian signature and the non-uniqueness of the Krein space of spinors

Abstract : We give examples illustrating the fact that the different space/time splittings of the tangent bundle of a semi-Riemannian spin manifold give rise to nonequivalent norms on the space of compactly supported sections of the spinor bundle, and as a result, to different completions. We give a necessary and sufficient condition for two space/time splittings to define equivalent norms in terms of a generalized Doppler shift between maximal negative definite subspaces. We explore some consequences for the noncommutative geometry program.
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Submitted on : Thursday, August 1, 2019 - 2:15:52 AM
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Fabien Besnard, Nadir Bizi. Doppler shift in semi-Riemannian signature and the non-uniqueness of the Krein space of spinors. J.Math.Phys., 2019, 60 (6), pp.063503. ⟨10.1063/1.5080525⟩. ⟨hal-02223029⟩

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