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

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) guage symmetries, including a subset of coordinates in the fundamental representation of the guage 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 guage symmetries which results in confinement-like phenomena.