Matter and light
Miguel Ballesteros,
(Technische Universität Braunschweig, Germany)
17/10/2013 12:00
Different objects interact with light in different ways and this permits us to distinguish their color. These processes can be understood only through quantum electrodynamics. Although a mathematical description of quantum electrodynamics is far beyond the scope of nowadays mathematics, the processes of emission and absorption of photons by atoms can be rigorously understood in the low-energy limit, if we neglect the creation and annihilation of electrons. The description of matter and light from the mathematical point of view relies on the study of eigenvalues of (non self-adjoint) operators, which are immersed in the continuum. In this presentation I report on new techniques, that allow us for the first time to study non-self-adjoint operators using multi-scale analysis (Pizzo, 2003). Our method is applied to the analysis of emission and absorption of photons by atoms. I further present a new approach to the Spectral Renormalization (Bach-Fröhlich-Sigal, 1998) in which a continuous flow of operators is constructed (in contrast to the discrete one used before), which satisfies a differential equation whose solution amounts to examine the eigenvalues. This last result is being completed. The talk is based on works in collaboration with Bach, Fröhlich and Pizzo.