Global symplectic potentials on the Witten covariant phase space for bosonic extendons

TL;DR

This paper proves that certain projections of deformation vectors act as global symplectic potentials on the covariant phase space of bosonic extendons, with a presymplectic structure invariant under diffeomorphisms.

Contribution

It establishes the role of deformation vector projections as global symplectic potentials and analyzes the structure's invariance under diffeomorphisms in the context of bosonic extendons.

Findings

Projections of deformation vectors serve as global symplectic potentials.

The presymplectic structure has no components tangent to diffeomorphism actions.

The structure is covariant and respects the background geometry.

Abstract

It is proved that the projections of the deformation vector field, normal and tangential to the worldsheet manifold swept out by Dirac-Nambu-Goto bosonic extendons propagating in a curved background, play the role of {\it global} symplectic potentials on the corresponding Witten covariant phase space. It is also proved that the {\it presymplectic} structure obtained from such potentials by direct exterior derivation, has not components tangent to the action of the relevant diffeomorphisms group of the theory.