Basic structures of the covariant canonical formalism for fields based on the De DonderWeyl theory
Abstract
We discuss a field theoretical extension of the basic structures of classical analytical mechanics within the framework of the De DonderWeyl (DW) covariant Hamiltonian formulation. The analogue of the symplectic form is argued to be the {\em polysymplectic} form of degree $(n+1)$, where $n$ is the dimension of spacetime, which defines a map between multivector fields or, more generally, graded derivation operators on exterior algebra, and forms of various degrees which play a role of dynamical variables. The SchoutenNijenhuis bracket on multivector fields induces the graded analogue of the Poisson bracket on forms, which turns the exterior algebra of (horizontal) forms to a Gerstenhaber algebra. The equations of motion are written in terms of the Poisson bracket on forms and it is argued that the bracket with $H\vol$, where $H$ is the DW Hamiltonian function and $\vol$ is the horizontal (i.e. spacetime) volume form, is related to the operation of exterior differentiation of forms.
 Publication:

arXiv eprints
 Pub Date:
 October 1994
 arXiv:
 arXiv:hepth/9410238
 Bibcode:
 1994hep.th...10238K
 Keywords:

 High Energy Physics  Theory
 EPrint:
 11 pages, Aachen preprint PITHA 94/47