Relativistic Virial Operators
Analysis of PDEs
2026-03-25 v1 Spectral Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2603.22947,
title = {Relativistic Virial Operators},
author = {Lucrezia Cossetti and Luca Fanelli and Fabio Pizzichillo},
journal= {arXiv preprint arXiv:2603.22947},
year = {2026}
}