A mathematical construction of the non-Abelian Chern-Simons functional integral
type: Item
instance of: scholarly article
title: A mathematical construction of the non-Abelian Chern-Simons functional integral
zbMATH Open document ID: 0889.58019
published in: Communications in Mathematical Physics
publication date: 1997-09-04T00:00:00Z
review text: Let CS be the Chern-Simons action functional on the space \({\mathcal A}\) of connections on a bundle over \(\mathbb{R}^3\). In this paper is given a realisation of normalised integrals of the form \(\int_{\mathcal A} e^{i\text{CS} (A)} \varphi(A) DA\) as \(\Phi_{\text{CS}} (\varphi)\), where \(\Phi_{\text{CS}}\) is an element of a Sobolev-type closure of a space \(L^2 (\mu)\). Properties of \(\Phi_{\text{CS}}\) are studied; in particular the moments are determined. Indications as to how these apply to knot theory are also given.
Mathematics Subject Classification ID: 58D30
Mathematics Subject Classification ID: 81T13
zbMATH DE Number: 1057289
zbMATH Keywords: Chern-Simons action functional
author: S. Albeverio
author: Ambar N. Sengupta
reviewed by: David B. Gauld
MaRDI profile type: Publication
full work available at URL: s002200050120
OpenAlex ID: W2025429719
DOI: 10.1007/S002200050120
description: scientific article; zbMATH DE number 1057289