Levinson's theorem: an index theorem in scattering theory

Thời gian: 15:00 đến 16:00 Ngày 23/10/2024

Địa điểm: Phòng C101, VIASM, 157 phố Chùa Láng, Hà Nội

Báo cáo viên: GS Serge Richard, Nagoya University, Japan

Tóm tắt: Levinson’s theorem is a relation between the number of bound states of a quantum mechanical system and an expression related to the scattering part of that system. During this seminar, we shall firstly recall the original version of this result, dating back to 1949. Subsequently, the framework of scattering theory will be introduced, and a more general version of this result will be presented. By using a C*-algebraic framework, it will then be shown that Levinson's theorem corresponds to an index theorem in scattering theory. This new perspective provides a better understanding of this relation, and opens the door to various generalizations. The main result will be illustrated with a few examples. No prior knowledge on scattering theory or on C*-algebras is necessary for this presentation.