International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 12, Pages 687-699
doi:10.1155/S0161171202013212

A geometrical analysis of the field equations in field theory

A. Echeverría-Enríquez, M. C. Muñoz-Lecanda, and N. Román-Roy

Departamento de Matem√°tica Aplicada IV., Edificio C-3, Campus Norte UPC., C/ Jordi Girona 1., Barcelona E-08034, Spain

Received 14 May 2001; Revised 6 September 2001

Copyright ¬© 2002 A. Echeverría-Enríquez et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We give a geometric formulation of the field equations in the Lagrangian and Hamiltonian formalisms of classical field theories (of first order) in terms of multivector fields. This formulation enables us to discuss the existence and nonuniqueness of solutions of these equations, as well as their integrability.