Physics – Mathematical Physics
Scientific paper
1999-07-07
J.Phys.A32:8461-8484,1999
Physics
Mathematical Physics
Some minor mistakes are corrected. Bibliography is updated. To be published in J. Phys. A: Mathematical and General
Scientific paper
10.1088/0305-4470/32/48/309
We state the intrinsic form of the Hamiltonian equations of first-order Classical Field theories in three equivalent geometrical ways: using multivector fields, jet fields and connections. Thus, these equations are given in a form similar to that in which the Hamiltonian equations of mechanics are usually given. Then, using multivector fields, we study several aspects of these equations, such as the existence and non-uniqueness of solutions, and the integrability problem. In particular, these problems are analyzed for the case of Hamiltonian systems defined in a submanifold of the multimomentum bundle. Furthermore, the existence of first integrals of these Hamiltonian equations is considered, and the relation between {\sl Cartan-Noether symmetries} and {\sl general symmetries} of the system is discussed. Noether's theorem is also stated in this context, both the ``classical'' version and its generalization to include higher-order Cartan-Noether symmetries. Finally, the equivalence between the Lagrangian and Hamiltonian formalisms is also discussed.
a-Enrí quez Echeverrí A.
Muñoz-Lecanda Miguel C.
Roy Román N.
No associations
LandOfFree
Multivector Field Formulation of Hamiltonian Field Theories: Equations and Symmetries does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Multivector Field Formulation of Hamiltonian Field Theories: Equations and Symmetries, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Multivector Field Formulation of Hamiltonian Field Theories: Equations and Symmetries will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-357822