Novel algebraic structures from the polysymplectic form in field theory

Abstract

The polysymplectic $(n+1)$-form is introduced as an analogue of the symplectic form for the De Donder-Weyl polymomentum Hamiltonian formulation of field theory. The corresponding Poisson brackets on differential forms are constructed. The analogues of the Poisson algebra are shown to be generalized (non-commutative and higher-order) Gerstenhaber algebras defined in the text.

6 pages, LaTeX. Talk at Gropu21, Goslar (Germany) 1996. Typos in math notation fixed, refs updated, minor style improvements

References in corpus (1)

• Cohomology and Deformation of Leibniz Pairs

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• Geometric (pre)quantization in the polysymplectic approach to field theory
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• $n$-plectic Maxwell Theory
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