Note on Self-Duality and the Kodama State

TL;DR

This paper explores the relationship between self-duality, the Kodama state, and knot invariants in quantum Abelian gauge theory, revealing that a self-dual CCR representation leads to the Kodama state as the vacuum.

Contribution

It demonstrates that choosing a self-dual CCR representation results in the Kodama state as the vacuum, linking self-duality with topological quantum states in Abelian gauge theory.

Findings

Self-dual CCR representation yields the Kodama state as vacuum

Connection established between self-duality and knot invariants

Implications for quantum topological states in gauge theories

Abstract

An interesting interplay between self-duality, the Kodama (Chern-Simons) state and knot invariants is shown to emerge in the quantum theory of an Abelian gauge theory. More precisely, when a self-dual representation of the CCR is chosen, the corresponding vacuum in the Schroedinger representation is precisely given by the Kodama state. Several consequences of this construction are explored.