Constraint characterization and degree of freedom counting in Lagrangian field theory
Verónica Errasti Díez, Markus Maier, Julio A. Méndez-Zavaleta
Abstract
We present a Lagrangian approach to counting degrees of freedom in first-order field theories. The emphasis is on the systematic attainment of a complete set of constraints. In particular, we provide the first comprehensive procedure to ensure the functional independence of all constraints and discuss in detail the possible closures of the constraint algorithm. We argue degrees of freedom can but need not correspond to physical modes. The appendix comprises fully worked out, physically relevant examples of varying complexity. Published by the American Physical Society 2024
Topics & Concepts
LagrangianField theory (psychology)Constraint (computer-aided design)Characterization (materials science)Degree (music)PhysicsField (mathematics)Classical mechanicsTheoretical physicsMathematicsMathematical physicsPure mathematicsGeometryOpticsAcousticsCosmology and Gravitation TheoriesGeometric Analysis and Curvature FlowsStochastic processes and financial applications