APEC Seminar (Astronomy - Particle Physics - Experimental Physics - Cosmology)

Speaker: Yu Jia (Institute of High Energy Physics, Beijing)
Title: Schrodinger, Klein-Gordon and Dirac equations, atomic wave functions and operator product expansion
Date (JST): Mon, Feb 18, 2019, 11:00 - 12:00
Place: Seminar Room A
Related File: 2250.pdf
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 the 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 equations. I will demonstrate that, somewhat
counterintuitively, the universal near-the-origin logarithmic
divergence of the Klein-Gordon and Dirac wave functions for 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 renormalization group equation.