Relativistic Virial Operators
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911541285093376 |
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| author | Cossetti, Lucrezia Fanelli, Luca Pizzichillo, Fabio |
| author_facet | Cossetti, Lucrezia Fanelli, Luca Pizzichillo, Fabio |
| contents | When studying Dirac operators, it is well known that the phenomenon of Zitterbewegung leads to a lack of convexity of the variance, which creates difficulties in the analysis of dispersive properties. In particular, standard virial methods are harder to implement in the Dirac setting. In this paper, we introduce a new approach based on the center-of-energy operator, leading to a family of relativistic virial identities. As an application, we establish spectral stability results for perturbed Dirac operators and prove local smoothing estimates for the associated evolution equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22947 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Relativistic Virial Operators Cossetti, Lucrezia Fanelli, Luca Pizzichillo, Fabio Analysis of PDEs Spectral Theory 81Q10, 81Q15, 35Q41 When studying Dirac operators, it is well known that the phenomenon of Zitterbewegung leads to a lack of convexity of the variance, which creates difficulties in the analysis of dispersive properties. In particular, standard virial methods are harder to implement in the Dirac setting. In this paper, we introduce a new approach based on the center-of-energy operator, leading to a family of relativistic virial identities. As an application, we establish spectral stability results for perturbed Dirac operators and prove local smoothing estimates for the associated evolution equation. |
| title | Relativistic Virial Operators |
| topic | Analysis of PDEs Spectral Theory 81Q10, 81Q15, 35Q41 |
| url | https://arxiv.org/abs/2603.22947 |