On The Geometry of Field Theoretic Gerstenhaber Structures

TL;DR

This paper explores the geometric structure underlying covariant Hamiltonian formulations of field theories, focusing on Gerstenhaber structures, symmetries, and the construction of a canonical 2-form in a fiber bundle setting.

Contribution

It provides a detailed geometric construction of Gerstenhaber structures for field theories on arbitrary fiber bundles, emphasizing naturality and symmetry treatment.

Findings

Gerstenhaber structure encodes equations of motion in covariant Hamiltonian formalism

Canonical 2-form derived via pull back and hypersurface integration

Framework applicable to arbitrary fiber bundles

Abstract

Field theoretical models with first order Lagrangean can be formulated in a covariant Hamiltonian formalism. In this article, the geometrical construction of the Gerstenhaber structure that encodes the equations of motion is explained for arbitrary fibre bundles. Special emphasis has been put on naturality of the constructions. Further, the treatment of symmetries is explained. Finally, the canonical field theoretical 2-form is obtained by pull back and integration of the polysymplectic form over space like hypersurfaces.