Complexified Lie Algebroids From a Generalized Stieltjes Action Approach to the Calculus of Variations - El-Nabulsi, Ahmad Rami; Wu, Guo-Cheng; Jamil, Mubasher (Sarajevo Journal of Mathematics, 2024)
In this work, we communicate the issue of Lie algebroids. More precisely, we discuss the subject based on the generalized Stieltjes fractal-like approach of the calculus of variations. We derived the corresponding Euler-Lagrange, geodesics and Wong’s equations and we illustrate then, by discussing, the resulted dynamics of a colored particle in Yang-Mills. Many motivating consequences are explored in particular, the emergence of complexified Lie algebroids with its corresponding complexified Lagrangian and Hamiltonian dynamics from the fractal approach. 2000 Mathematics Subject Classification. 49S05, 26A33, 20L05