Non-Abelianizable First Class Constraints

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.

minor corrections, to appear in Communications in Mathematical Physics

References in corpus (3)

• Non-perturbative Faddeev-Popov formula and infrared limit of QCD
• Abelian Subset of Second Class Constraints
• Abelianization of First Class Constraints

Cited by in corpus (4)

• Dirac-Bergmann Constraints in Physics: Singular Lagrangians, Hamiltonian Constraints and the Second Noether Theorem
• Gribov ambiguity and degenerate systems
• Formulation of singular theories in a partial Hamiltonian formalism using a new bracket and multi-time dynamics
• Gauge symmetries of systems with a finite number of degrees of freedom