Involutive constrained systems and Hamilton-Jacobi formalism
M. C. Bertin, B. M. Pimentel, C. E. Valc\'arcel
TL;DR
This paper explores the Hamilton-Jacobi formalism for singular systems with involutive constraints, linking Frobenius' theorem, canonical transformations, and gauge symmetries to deepen understanding of constrained Hamiltonian dynamics.
Contribution
It establishes a novel connection between Frobenius' theorem, involutive constraints, and gauge transformations within the Hamilton-Jacobi framework.
Findings
Demonstrates the relationship between involutive constraints and gauge transformations.
Links Frobenius' theorem to the structure of singular systems.
Provides a unified view of canonical transformations and gauge symmetries.
Abstract
In this paper, we study singular systems with complete sets of involutive constraints. The aim is to establish, within the Hamilton-Jacobi theory, the relationship between the Frobenius' theorem, the infinitesimal canonical transformations generated by constraints in involution with the Poisson brackets, and the lagrangian point (gauge) transformations of physical systems.
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