Comment on "Dimension of the Moduli Space and Hamiltonian Analysis of BF Field Theories"

TL;DR

This paper comments on existing methods for analyzing BF field theories, emphasizing their general applicability to various Lie algebras with non-degenerate invariant inner products, and clarifies their relevance to different gauge groups.

Contribution

It highlights that the results on canonical analysis and constraint transformations are broadly applicable beyond specific cases, extending to any Lie algebra with a suitable inner product.

Findings

Results are generic for any Lie algebra with a non-degenerate invariant inner product.

The analysis applies to both coupled and uncoupled BF theories with different gauge groups.

The methods unify the treatment of BF theories across various Lie algebras.

Abstract

The purpose of this Comment is to point out that the results presented in the appendix of M. Mondragon and M. Montesinos, J. Math. Phys. 47, 022301 (2006) provides a generic method so as to deal with cases as those of Section 6 of R. Cartas-Fuentevilla, A. Escalante-Hern\'andez, and J. Berra-Montiel, Int. J. Mod. Phys. A 26, 3013 (2011). The results already reported are: the canonical analysis, the transformations generated by the constraints, and the analysis of the reducibility of the constraints for SO(3,1) and SO(4) four-dimensional BF theory coupled or not to a cosmological constant. But such results are generic and hold actually for any Lie algebra having a non-degenerate inner product invariant under the action of the gauge group.