×

Complexified Lie algebroids from a generalized Stieltjes action approach to the calculus of variations. (English) Zbl 1255.49079

Summary: 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 derive the corresponding Euler-Lagrange, geodesics and Wongs equations and we then illustrate, by discussing, the resulting dynamics of a colored particle in the Yang-Mills field. Many motivating conseuqences are explored, in particular the emergence of complexified Lie algebroids with its corresponding complexified Lagrangian and Hamiltonian dynamics from the fractal approach.

MSC:

49S05 Variational principles of physics
49J20 Existence theories for optimal control problems involving partial differential equations
20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms)
26A33 Fractional derivatives and integrals
PDFBibTeX XMLCite