Abstract:

 

'Microlocal' stands for localization in the location and the frequency, and the 'second microlocalization' stands for a further refined localization. 

 

I will discuss how we implement this idea, and how to use this, in combination with the Fredholm machinery to derive the fact that solutions to the Klein-Gordon equation, after suitable modulation, degenerates to solutions to the Schrodinger equation in the limit c (the speed of light) tends to infinity. The main novelty of this work is that we can obtain both the microlocal convergence and the global in spacetime convergence; in addition, we are able to encode the particle and the anti-particle solutions simultaneously in a very natural manner.

(This is based on a joint work with Andrew Hassell, András Vasy, Ethan Sussman.)