Non-Abelianizable First Class Constraints
High Energy Physics - Theory
2016-09-06 v5
Abstract
We study the necessary and sufficient conditions on Abelianizable first class constraints. The necessary condition is derived from topological considerations on the structure of gauge group. The sufficient condition is obtained by applying the theorem of implicit function in calculus and studying the local structure of gauge orbits. Since the sufficient condition is necessary for existence of proper gauge fixing conditions, we conclude that in the case of a finite set of non-Abelianizable first class constraints, the Faddeev-Popov determinant is vanishing for any choice of subsidiary constraints. This result is explicitly examined for SO(3) gauge invariant model.
Keywords
Cite
@article{arxiv.hep-th/0303014,
title = {Non-Abelianizable First Class Constraints},
author = {Farhang Loran},
journal= {arXiv preprint arXiv:hep-th/0303014},
year = {2016}
}
Comments
minor corrections, to appear in Communications in Mathematical Physics