佐賀大学理工学部
第192回応数談話会

日時

2007年2月22日 （木曜日）16：10−17：10

講演者

A. Hahn 氏（Universität Bonn）

題目

From path integrals to topological invariants of 3-manifolds

概要

The study of the heuristic Chern-Simons path integral by E. Witten inspired (at least) two general approaches to the theory of ``quantum" 3- manifold invariants. 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 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, using White Noise Analysis, 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＠]
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