佐賀大学理工学部
第184回応数談話会

談話会

日時

2006年2月6日（月）16：00−17：00

講演者

Atle Hahn氏(Universität Bonn)

題目

From path integrals to the Reshetikhin-Turaev invariants

概要

The study of the heuristic Chern-Simons path integral by E. Witten inspired (at least) two general approaches to quantum topology. Firstly, the perturbative approach based on the CS path integral in the Lorentz gauge and, secondly, the "quantum group approach" by Reshetikhin/Turaev. While for the first approach the relation to the CS path integral is obvious for the second approach it is not. In particular, it is not clear if/how one can derive the relevant R-matrices or quantum 6j-symbols directly from the CS path integral. In my talk, which summarizes the results of a recent preprint, I will sketch a strategy that should lead to a clarification of this issue in the special case where the base manifold is of product form. This strategy is based on the "torus gauge fixing" procedure introduced by Blau/Thompson for the study of the partition function of CS models. I will show that the formulas of Blau/Thompson can be generalized to Wilson lines and that the evaluation of the expectation values of these Wilson lines leads to the same state sum expressions in terms of which Turaev's shadow invariant is defined. Finally, I will sketch how one can obtain a rigorous realization of the path integral expressions appearing in this treatment.

場所

数理科学科大セミナー室（理工学部6号館(DC棟)5階501号室）

連絡先

〒840-8502 佐賀市本庄町1 佐賀大学理工学部数理科学科
三苫　至 [mitoma＠]
TEL 0952-28-8526 　FAX 0952-28-8501

大学院集中講義(関数解析学特論II)

日時

2006年2月6日(月)11：00−12：30

内容

An Introduction to Chern-Simons Theory