MULTISYMPLECTIC GEOMETRY AND k-COSYMPLECTIC STRUCTURE FOR THE FIELD THEORIES AND THE RELATIVISTIC MECHANICS

Abstract

The aim of this work is twofold: First, we extend the multisymplectic geometry already done for field theories to the relativistic mechanics by introducing an appropriate configuration bundle. In particular, we developed the model to obtain the Hamilton–De Donder–Weyl equations to the movement of a relativistic charged particle immerged in an electromagnetic field. Second, we have found a direct relationship between the multisymplectic geometry and the k-cosymplectic structure of a physical system.