| Abstract: |
| The non-relativistic limit for a Klein-Gordon equation, with electric and magnetic potential terms on a Lorentzian manifold, corresponds to a family of Lorentzian metrics for which, with respect to an appropriate spacelike foliation of the manifold, the speed of light tends to infinity. Concretely, we consider decaying, both in spacetime and as $c\to+\infty$, perturbations of the Minkowski metric, $-c^2 dt^2+dx^2$, with spacetime decaying electric and magnetic potentials on $\mathbb{R}^{1,d}$; this is interesting already if the metric is just the $c$-dependent Minkowski metric. We give a complete and unified phase space analysis of the solution operators for the inhomogeneous wave equation as $c\to\infty$. In some regimes these tend to the Minkowski Klein-Gordon propagators, but in others (spatially low frequency) two copies of the Schr\{o}dinger propagator emerges, with electric and magnetic potentials, but on flat space, as expected from the standard physical treatment. Joint work with Andrew Hassell, Qiuye Jia and Ethan Sussman; the talk will emphasize the microlocal ingredients of the project, as in arXiv:2509.09518, see arXiv:2511.08724 for the applications. |
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