## Noether charge in multisymplectic geometry

Hi,

I'm currently looking for the mathematical foundation behind the
claim, often found in field theory/string theory books that the
noether charge associated to a symmetry of the lagrangian is the
generator of that symmetry, ie. its poisson bracket with a field from
the lagrangian, generates the change in the field.

Recently I came across the article 'Covariant Momentum maps & field
theory part I/II' by Gotay and Marsden. In there I've found that the
concept of a Noether current is in fact given by the covariant
momentum map in the multisymplectic classical field theory
formulation. In particular, this map satisfies the mathematical analog
of noether's theorem as explained in the article.

In part II of the article they define an instantaneous momentum map,
loosely defined by the integral of the covariant momentum map over a
cauchy hypersurface. My question is now, whether this is the
mathematical object that corresponds to the Noether charge (which in
physics is defined as the integral of the time component of the
current over a spacelike hypersurface)? Moreover, if that is so,
somehow I still can't find an explicit demonstration (in the above
article or any other mathematical article) that this charge then
generates the transformation, ie is somehow related to the generators
of the Lie algebra of the Lie group that encodes the symmetry.

Could anyone help me out on clarifying these matters?