Wednesday, November 22, 2023 - 16:00 in U2-232
The massless and the non-relativistic limit for the cubic Dirac equation
A talk in the Oberseminar Analysis series by
Timothy Candy
| Abstract: |
The Dirac equation is the relativistic version of the Schrödinger equation, and hence unsurprisingly it plays a central role in relativistic (where the speed of light is finite) quantum mechanics. It is known that for certain nonlinear models, as the speed of light tends to infinity, the Dirac equation converges on finite time scales to a Schrödinger equation.
Here I will explain how recent uniform (in the speed of light) estimates for small data solutions to the cubic Dirac equation can be used to prove that the non relativistic limit in fact holds on global time scales. In particular we have convergence of scattering states and wave operators for the Dirac equation, to the corresponding Schrödinger equation.
This is joint work with Sebastian Herr.
Within the CRC this talk is associated to the project(s): A1 |
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