Symplectic Quantum Mechanics and Chern-Simons Gauge Theory I

TL;DR

This paper explores the connection between Chern-Simons gauge theory and symplectic quantum mechanics, demonstrating their partition functions' equivalence and providing a semiclassical formula for the symplectic approach.

Contribution

It establishes the equivalence of partition functions from Chern-Simons theory and symplectic action functional, offering a new semiclassical formula for the latter.

Findings

Partition functions from both Lagrangians agree.

Identified semiclassical formula for symplectic partition function.

Clarified the relation between gauge theory and symplectic mechanics.

Abstract

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 two Lagrangians agree, and we identify the semiclassical formula for the partition function defined using the symplectic action functional.