Dirac operators and local invariants on perturbations of Minkowski space
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915068884549632 |
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| author | Dang, Nguyen Viet Vasy, András Wrochna, Michał |
| author_facet | Dang, Nguyen Viet Vasy, András Wrochna, Michał |
| contents | For small perturbations of Minkowski space, we show that the square of the Lorentzian Dirac operator $P= -D^2$ has real spectrum apart from possible poles in a horizontal strip. Furthermore, for $\varepsilon>0$ we relate the poles of the spectral zeta function density of $P-i\varepsilon$ to local invariants, in particular to the Lorentzian scalar curvature. The proof involves microlocal propagation and radial estimates in a resolved scattering calculus as well as high energy estimates in a further resolved classical-semiclassical calculus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12714 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dirac operators and local invariants on perturbations of Minkowski space Dang, Nguyen Viet Vasy, András Wrochna, Michał Analysis of PDEs Mathematical Physics For small perturbations of Minkowski space, we show that the square of the Lorentzian Dirac operator $P= -D^2$ has real spectrum apart from possible poles in a horizontal strip. Furthermore, for $\varepsilon>0$ we relate the poles of the spectral zeta function density of $P-i\varepsilon$ to local invariants, in particular to the Lorentzian scalar curvature. The proof involves microlocal propagation and radial estimates in a resolved scattering calculus as well as high energy estimates in a further resolved classical-semiclassical calculus. |
| title | Dirac operators and local invariants on perturbations of Minkowski space |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2412.12714 |