On singular Lagrangians affine in velocities
Jos\'e F. Cari\~nena, Jos\'e Fern\'andez-N\'u\~nez, Manuel F., Ra\~nada
TL;DR
This paper provides a geometric analysis and classification of singular Lagrangians affine in velocities, highlighting their gauge invariance and constraint structures.
Contribution
It offers a comprehensive geometric framework and classification for singular affine-in-velocity Lagrangians, emphasizing their gauge invariance.
Findings
All such Lagrangians are necessarily singular.
They generally exhibit gauge invariance.
A complete classification of these Lagrangians is achieved.
Abstract
The properties of Lagrangians affine in velocities are analyzed in a geometric way. These systems are necessarily singular and exhibit, in general, gauge invariance. The analysis of constraint functions and gauge symmetry leads us to a complete classification of such Lagrangians.
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