Coordinate Singularities of Self-Interacting Vector Field Theories
Andrew Coates, Fethi M. Ramazanoğlu
Abstract
Self-interacting vectors are seeing a burst of interest where various groups demonstrated that the field evolution ends in finite time. Two nonequivalent criteria have been offered to identify this breakdown: (i) the vector constraint equation cannot be satisfied beyond a point where the breakdown occurs, (ii) the dynamics is governed by an effective metric that becomes singular at the breakdown. We show that (i) identifies a coordinate singularity, and can be removed by a change of coordinates. Hence, it does not signify a physical problem, and cannot determine the validity of a theory.
Topics & Concepts
SingularityGravitational singularityPhysicsField theory (psychology)Constraint (computer-aided design)Metric (unit)Vector fieldField (mathematics)Coordinate systemPoint (geometry)Classical mechanicsSingular point of a curveTheoretical physicsMathematical physicsStatistical physicsMathematical analysisMathematicsPure mathematicsQuantum mechanicsGeometryMechanicsEconomicsOperations managementQuantum Electrodynamics and Casimir EffectNonlinear Dynamics and Pattern FormationCosmology and Gravitation Theories