102 research outputs found
A geometrical analysis of the field equations in field theory
In this review paper we give a geometrical 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 non-uniqueness of solutions, as well as their
integrability.Comment: 14 pages. LaTeX file. This is a review paper based on previous works
by the same author
The Hamilton-Jacobi Formalism for Higher Order Field Theories
We extend the geometric Hamilton-Jacobi formalism for hamiltonian mechanics
to higher order field theories with regular lagrangian density. We also
investigate the dependence of the formalism on the lagrangian density in the
class of those yelding the same Euler-Lagrange equations.Comment: 25 page
Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories
This review paper is devoted to presenting the standard multisymplectic formulation for describing geometrically classical field theories, both the regular and singular cases. First, the main features of the Lagrangian formalism are revisited and, second, the Hamiltonian formalism is constructed using Hamiltonian sections. In both cases, the variational principles leading to the Euler-Lagrange and the Hamilton-De Donder-Weyl equations, respectively, are stated, and these field equations are given in different but equivalent geometrical ways in each formalism. Finally, both are unified in a new formulation (which has been developed in the last years), following the original ideas of Rusk and Skinner for mechanical systems
On Higher Derivatives as Constraints in Field Theory: a Geometric Perspective
We formalize geometrically the idea that the (de Donder) Hamiltonian
formulation of a higher derivative Lagrangian field theory can be constructed
understanding the latter as a first derivative theory subjected to constraints.Comment: 7 page
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