RTG Seminar Leipzig

Asymptotic completeness of N-body scattering

by Prof. Jan Derezinski ((University of Warsaw))


This is the first lecture within a compact lecture course organized within the Emmy-Noether research program by Daniela Cadamuro at Leipzig.




In my lectures I will describe the basic formalism of 2- and N-body  
scattering theory, both in the short-range and long-range case. I will 
also discuss the main ideas of the proof of asymptotic completeness. My 
lectures will follow the monograph

J.Dereziński and C. Gerard "Scattering Theory of Classical and Quantum 
N-Particle Systems" Springer

Tracts and Monographs in Physics, 1997, available at 
The monograph uses the ideas of

I.M. Sigal: On the long-range scattering, Duke Math.Journal 60 (1990) 

I.M. Sigal, A. Soffer: The N-particle scattering problem: asymptotic 
completeness for short-range quantum systems, Ann. of Math. 125 (1987) 

G.M. Graf: Asymptotic completeness for N-body short-range systems: A new 
proof, Comm. Math. Phys. 132 (1990) 73-101

J. Dereziński: Asymptotic completeness fo; independently on the research 
they do, it will be very instructiver N-body long-range quantum systems, 
Ann. of Math. 138 (1993) 437-473

Proving asymptotic completeness of N-body scattering is a great 
achievement of 20th century mathematical physics. It settled in a very 
satisfactory way a question important for nonrelativistic quantum 
physics and quantum chemistry.
The proof involves several very  ingenious arguments, which on the one 
hand are complex and technical, on the other hand are intuitive and 
beautiful. I believe that even those who do not plan to actively engage 
in  research on N-body scattering will benefit from learning these 
arguments, since they involve many important concepts of mathematical 
physics, such as classical limit of quantum dynamics and the structure 
of N-body systems.
The prerequisites of the course are modest: basic classical and quantum 
mechanics as well as elements of the  theory of operators on Hilbert 


It consists of a series of 4 online lectures, taking place at the 
following dates:

Week 1:

Wed 30/06, 10:00 - 11:30 CET

Fri 02/07, 14:00 - 15:30 CET

Week 2:

Wed 07/07, 10:00 - 11:30 CET

Fri 09/07, 14:00 - 15:30 CET

The lecture can be accessed via Zoom, at a link that will be provided 
in advance.