Gauge transformations for higher-order lagrangians
Xavier Gracia (Politechnic University of Catalonia) Josep M. Pons, (University of Barcelona)
TL;DR
This paper investigates gauge transformations in higher-order Lagrangian systems, providing a characterization useful for singular cases and illustrating the concepts with examples, including relativistic particle models.
Contribution
It introduces a new characterization of Noether's symmetry transformations for higher-order Lagrangians, especially for singular cases, with detailed analysis of second-order systems.
Findings
Characterization of symmetry transformations for higher-order Lagrangians
Identification of gauge transformations in second-order systems
Example of gauge transformations in relativistic particle with curvature
Abstract
Noether's symmetry transformations for higher-order lagrangians are studied. A characterization of these transformations is presented, which is useful to find gauge transformations for higher-order singular lagrangians. The case of second-order lagrangians is studied in detail. Some examples that illustrate our results are given; in particular, for the lagrangian of a relativistic particle with curvature, lagrangian gauge transformations are obtained, though there are no hamiltonian gauge generators for them.
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