We compute the semiclassical formulas for the partition functions obtained using two different Lagrangians: the Chern-Simons functional and the symplectic action functional.
In this article we describe the relation between the Chern-Simons gauge theory partition function and the partition function defined using the symplectic action functional as the Lagrangian. We show that the partition functions obtained using these t
wo Lagrangians agree, and we identify the semiclassical formula for the partition function defined using the symplectic action functional.
This paper studies U(1)-Chern-Simons theory and its relation to a construction of Chris Beasley and Edward Witten. The natural geometric setup here is that of a three-manifold with a Seifert structure. Based on a suggestion of Edward Witten we are le
d to study the stationary phase approximation of the path integral for U(1)-Chern-Simons theory after one of the three components of the gauge field is decoupled. This gives an alternative formulation of the partition function for U(1)-Chern-Simons theory that is conjecturally equivalent to the usual U(1)-Chern-Simons theory. The goal of this paper is to establish this conjectural equivalence rigorously through appropriate regularization techniques. This approach leads to some rather surprising results and opens the door to studying hypoelliptic operators and their associated eta invariants in a new light.
This article studies the nonabelian localization results of Beasley and Witten, and considers the analogue of these results when the gauge group is U(1). It compares these results with results of Manoliu on abelian Chern-Simons theory, showing that t
he dependence on the coupling constant is the same.
