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arXiv · 2308.12057

The massless and the non-relativistic limit for the cubic Dirac equation

Timothy Candy·Sebastian Herr
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Abstract

Massive and massless Dirac equations with Lorentz-covariant cubic nonlinearities are considered in spatial dimension $d=2,3$. Global well-posedness of the Cauchy problem for small initial data in scale-invariant Sobolev spaces and scattering of solutions is proved by a new approach which uses bilinear Fourier restriction estimates and atomic function spaces. Furthermore, global uniform convergence results, both in the massless and in the non-relativistic limit, are proved at optimal regularity. In both regimes, these are the first results which imply convergence of scattering states and wave operators.

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Timothy Candy, Sebastian Herr. 2023-08-23. The massless and the non-relativistic limit for the cubic Dirac equation. https://arxiv.org/abs/2308.12057

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