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

Fabien Besnard (1) , Nadir Bizi (2)

1 EPF - Ecole Polytechnique Féminine
2 IMPMC - Institut de minéralogie, de physique des matériaux et de cosmochimie

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.

Domaines: Physique mathématique [math-ph]

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⟩