Signature change by a morphism of spectral triples
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915826051842048 |
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| author | Nieuviarts, Gaston |
| author_facet | Nieuviarts, Gaston |
| contents | We present a connection between twisted spectral triples and pseudo-Riemannian spectral triples, rooted in the fundamental interplay between twists and Krein products. A concept of morphism of spectral triples is introduced, transforming one spectral triple into its dual. In the case of even-dimensional manifolds, we demonstrate how this construction implements a local signature change via the parity operator induced by the twist. Consequently, the signature change transformation is governed solely by the unitary operator that implements the twist. This unitary is a central element of our approach, as it is directly linked to the Krein product, the twist, and the parity operator that implements the signature change. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05839 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Signature change by a morphism of spectral triples Nieuviarts, Gaston Mathematical Physics We present a connection between twisted spectral triples and pseudo-Riemannian spectral triples, rooted in the fundamental interplay between twists and Krein products. A concept of morphism of spectral triples is introduced, transforming one spectral triple into its dual. In the case of even-dimensional manifolds, we demonstrate how this construction implements a local signature change via the parity operator induced by the twist. Consequently, the signature change transformation is governed solely by the unitary operator that implements the twist. This unitary is a central element of our approach, as it is directly linked to the Krein product, the twist, and the parity operator that implements the signature change. |
| title | Signature change by a morphism of spectral triples |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2402.05839 |