Field: Theoretical Physics and Astrophysics

Supervisor’s Name: Jana Musilová

Doctoral Thesis Subject Title (2008/09):

Variational Sequences: A Useful Tool  of Mathematical Physics

Subject brief characteristics:

Variational sequence on finite order jet prolongations of fibred manifolds with one-dimensional or multi-dimensional bases forms a suitable geometrical structure to describe physical systems in mechanics or field theory. It is a very powerful mathematical tool to identify a trivial variational problem  (trivial lagrangians resulting in identically zero left- hand sides of equations of motion) and variationality of equations of motion (variational equations are derived from lagrangians). Thesis objective is to focus on practical applications of variational sequences on finite order prolongations of fibred manifolds primarily to explore variationality of particular physical systems in mechanics and field theory. 

List of basic references:

[1] Krupka D.: Variational Sequences on Finite Order Jet Spaces. In: Differential Geometry and its Applictions. Proc. Conf. August 27 - September 2, 1989, Brno, Czechoslovakia. World Scientific, Singapore, 1990, 236-254.

[2] Krbek M., Musilová J.: Representation of the Variational Sequence by Differential Forms. Acta Applicandae Mathematicae 88 (2005), 177-199. And selected publications quoted herein.

[3] More references chosen to comply selected issues.