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 non-equivalent 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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Cited by in corpus (2)

• Noncommutative geometry, the Lorentzian Standard Model and its B-L extension
• A $U(1{)}_{B-L}$-extension of the Standard Model from Noncommutative Geometry