Yang- Mills on Quantum Heisenberg Manifolds

TL;DR

This paper demonstrates that for quantum Heisenberg manifolds, the two variations of the Yang-Mills action functional in noncommutative geometry are equivalent, clarifying their relationship.

Contribution

It establishes the equivalence of two different formulations of Yang-Mills action functionals on quantum Heisenberg manifolds.

Findings

The two variations of Yang-Mills action functional agree on quantum Heisenberg manifolds.

Clarifies the relationship between different noncommutative geometric approaches.

Provides insights into gauge theories on noncommutative spaces.

Abstract

In the noncommutative geometry program of Connes there are two variations of the concept of Yang-Mills action functional. We show that for the quantum Heisenberg manifolds they agree.