The NoetherBesselHagen symmetry approach for dynamical systems
Abstract
The NoetherBesselHagen theorem can be considered a natural extension of Noether Theorem to search for symmetries. Here, we develop the approach for dynamical systems introducing the basic foundations of the method. Specifically, we establish the NoetherBesselHagen analysis of mechanical systems where external forces are present. In the second part of the paper, the approach is adopted to select symmetries for a given systems. In particular, we focus on the case of harmonic oscillator as a testbed for the theory, and on a cosmological system derived from scalartensor gravity with unknown scalarfield potential V (φ). We show that the shape of potential is selected by the presence of symmetries. The approach results particularly useful as soon as the Lagrangian of a given system is not immediately identifiable or it is not a Lagrangian system.
 Publication:

International Journal of Geometric Methods in Modern Physics
 Pub Date:
 2020
 DOI:
 10.1142/S0219887820502151
 arXiv:
 arXiv:2003.13756
 Bibcode:
 2020IJGMM..1750215U
 Keywords:

 Lagrangian;
 Noether symmetry approach;
 Noether–BesselHagen symmetry;
 invariant differential form;
 fibered mechanics;
 extended gravity cosmology;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 26 pages