Non-Abelianizable First Class Constraints

Details Non-Abelianizable First Class Constraints Non-Abelianizable First Class Constraints

2003-03-03

arxiv.org/abs/hep-th/0303014v5

Commun.Math.Phys.254:167-178,2005

Physics

High Energy Physics

High Energy Physics - Theory

minor corrections, to appear in Communications in Mathematical Physics

Scientific paper

10.1007/s00220-004-1248-7

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.

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