GAUGE SYMMETRIES OF SYSTEMS WITH A FINITE NUMBER OF DEGREES OF FREEDOM

Abstract

For systems with a finite number of degrees of freedom, it is shown in a paper [Commun Math. Phys.254, 167 (2005), arXiv:hep-th/0303014] that first-class constraints are Abelianizable if the Faddeev–Popov determinant is not vanishing for some choice of subsidiary constraints. Here, for irreducible first-class constraint systems with SO(3) or SO(4) gauge symmetries, including a subset of coordinates in the fundamental representation of the gauge group, we explicitly determine the Abelianizable and non-Abelianizable classes of constraints. For the Abelianizable class, we explicitly solve the constraints to obtain the equivalent set of Abelian first-class constraints. We show that for non-Abelianizable constraints there exist residual gauge symmetries which results in confinement-like phenomena.