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• W1644904578 abstract "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 $Hvol$, 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." @default.
• W1644904578 created "2016-06-24" @default.
• W1644904578 creator A5084260523 @default.
• W1644904578 date "1994-10-31" @default.
• W1644904578 modified "2023-09-27" @default.
• W1644904578 title "Basic structures of the covariant canonical formalism for fields based on the De Donder--Weyl theory" @default.
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