Faddeev-Jackiw Analysis of Topological Mass Generating Action

TL;DR

This paper uses Faddeev-Jackiw analysis to study the gauge symmetry of a topological mass generating action involving vector and antisymmetric tensor fields, revealing how auxiliary fields can enhance and modify symmetry properties.

Contribution

It demonstrates how the Faddeev-Jackiw formalism can analyze gauge symmetry changes in topological mass actions, especially the role of auxiliary fields in non-Abelian cases.

Findings

In Abelian case, the system induces mass while preserving gauge symmetry.

In non-Abelian case, auxiliary fields are needed to restore gauge symmetry.

Enhanced gauge symmetry becomes reducible with auxiliary fields.

Abstract

We analyze the gauge symmetry of a topological mass generating action in four dimensions which contains both a vector and a second rank antisymmetric tensor fields. In the Abelian case, this system induces an effective mass for the vector gauge field via a topological coupling $B \wedge F$ in the presence of a kinetic term for the antisymmetric tensor field $B$, while maintaining a gauge symmetry. On the other hand, for the non-Abelian case the $B$ field does not have a gauge symmetry unless an auxiliary vector field is introduced to the system. We analyze this change of symmetry in the Faddeev-Jackiw formalism, and show how the auxiliary vector field enhances the symmetry. At the same time this enhanced gauge symmetry becomes reducible. We also show this phenomenon in this analysis.