On the Canonical Structure of the De DonderWeyl Covariant Hamiltonian Formulation of Field Theory I. Graded Poisson brackets and equations of motion
Abstract
The analogue of the Poisson bracket for the De DonderWeyl (DW) Hamiltonian formulation of field theory is proposed. We start from the Hamilton PoincaréCartan (HPC) form of the multidimensional variational calculus and define the bracket on the differential forms over the spacetime (=horizontal forms). This bracket is related to the SchoutenNijenhuis bracket of the multivector fields which are associated with the horizontal forms by means of the "polysymplectic form". The latter is given by the HPC form and generalizes the symplectic form to field theory. We point out that the algebra of forms with respect to our Poisson bracket and the exterior product has the structure of the Gerstenhaber graded algebra. It is shown that the Poisson bracket with the DW Hamiltonian function generates the exterior differential thus leading to the bracket representation of the DW Hamiltonian field equations. Few illustrative examples are also presented.
 Publication:

arXiv eprints
 Pub Date:
 December 1993
 arXiv:
 arXiv:hepth/9312162
 Bibcode:
 1993hep.th...12162K
 Keywords:

 High Energy Physics  Theory
 EPrint:
 LATEX, 30 pages, PITHA 93/41