New math can finally track the weird 'trembling' move that high-speed particles do, which usually breaks every physics model we have.
March 25, 2026
Original Paper
Relativistic Virial Operators
arXiv · 2603.22947
The Takeaway
According to the Dirac equation, fundamental particles like electrons don't move in smooth lines but exhibit 'Zitterbewegung'—an erratic, high-speed jittery motion. This paper introduces a 'center-of-energy' operator that stabilizes calculations of this trembling, allowing physicists to prove the stability of these jittery particles in complex environments where they previously appeared chaotic.
From the 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 Dir