Basic structures of the covariant canonical formalism for fields based on the De Donder--Weyl theory
| dc.creator | Kanatchikov, Igor V. | |
| dc.date | 1994-10-31 | |
| dc.date.accessioned | 2026-07-07T04:20:43Z | |
| dc.date.available | 2026-07-07T04:20:43Z | |
| dc.description | We discuss a field theoretical extension of the basic structures of classical analytical mechanics within the framework of the De Donder--Weyl (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 space-time, 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 Schouten-Nijenhuis 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. space-time) volume form, is related to the operation of exterior differentiation of forms. | |
| dc.description | 11 pages, Aachen preprint PITHA 94/47 | |
| dc.identifier | https://arxiv.org/abs/hep-th/9410238 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9410238 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/54041 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Basic structures of the covariant canonical formalism for fields based on the De Donder--Weyl theory | |
| dc.type | text |