Gauge equivalence and conserved quantities for Lagrangian systems on Lie algebroids
J.F. Cari\~nena, Miguel Rodriguez-Olmos
TL;DR
This paper develops a theory of gauge and dynamical equivalence for Lagrangian systems on Lie algebroids, exploring their connection with conserved quantities arising from symmetries.
Contribution
It introduces a novel framework linking gauge and dynamical equivalence with conserved quantities in Lie algebroid-based Lagrangian systems.
Findings
Established a relationship between gauge transformations and conserved quantities.
Extended Noether's theorem to systems on Lie algebroids.
Provided a unified approach to symmetries and conservation laws in this setting.
Abstract
We develop a theory of gauge and dynamical equivalence for Lagrangian systems on Lie algebroids, also studying its relationship with Noether and non-Noether conserved quantities.
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