On a minimum of Yang-Mills functional on quantum Heisenberg manifolds

TL;DR

This paper investigates the Yang-Mills functional on quantum Heisenberg manifolds, identifying new critical points that differ from previously known solutions, using noncommutative geometric methods.

Contribution

It introduces novel critical points of the Yang-Mills functional on quantum Heisenberg manifolds, expanding understanding of its minima in noncommutative geometry.

Findings

A connection on a projective module over quantum Heisenberg manifolds is a minimum of Yang-Mills functional.

Discovered critical points differ from those previously found by S. Kang.

Uses Connes and Rieffel's apparatus for analysis.

Abstract

In this paper, we study the Yang-Mills functional on quantum Heisenberg manifolds using the appratuses developed by A. Connes and M. Rieffel. It is discovered that a connection on a projective module over a quantum Heisenberg manifold is a minimum of Yang-Mills functional whicih is a critical point that is different with critical points found by S. Kang.