Time & Place: Dec 28, 3:00pm, Room 9409

Speaker: Prof. Yu Jia (贾宇), Institute of High Energy Physics

Title: Schrodinger, Klein-Gordon and DIrac equations, atomic wave
functions and operator product expansion

Abstract: Effective field theory (EFT) and operator product expansion
(OPE) are two modern tools in the realm of theoretical high energy
physics. In this talk, I show these two powerful methods can also
provide novel perspective for understanding the short-range features of
atomic wave functions. In the first half of the talk, I will start from
the nonrelativistic Coulomb-Schrodinger EFT, then employ OPE to
investigate the universal electron-nucleus coalescence behavior of
atomic wave functions. An exact OPE relation is proved to all orders in
perturbation theory.  In the second part of the talk, I will show how to
solve a 90-year-old puzzle in relativistic quantum mechanics, which is
related to the Coulomb solutions of Klein-Gordon and Dirac equation. I
will demonstrate that, somewhat counterintuitively, the universal
near-the-origin logarithmic divergence of the Klein-Gordon and Dirac
wave functions of the S-wave hydrogen atoms, can not be addressed in the
relativistic QED, but can be satisfactorily understood in the framework
of nonrelativistic EFT with the aid of OPE and RGE.