Note on the bundle geometry of field space, variational connections, the dressing field method, & presymplectic structures of gauge theories over bounded regions

Understand

In this note, we consider how the bundle geometry of field space interplays with the covariant phase space methods so as to allow to write results of some generality on the presymplectic structure of invariant gauge theories coupled to matter.

• We obtain in particular the generic form of Noether charges associated with field-independent and field-dependent gauge parameters, as well as their Poisson bracket.
• We also provide the general field-dependent gauge transformations of the presymplectic potential and 2-form, which clearly highlight the problem posed by boundaries in generic situations.
• We then conduct a comparative analysis of two strategies recently considered to evade the boundary problem and associate a modified symplectic structure to a gauge theory over a bounded regions: namely the use of edge modes on the one hand, and of variational connections on the other.