  Soft symmetries for Yang-Mills theory are shown to correspond to the residual
Hamiltonian action of the gauge group on the Ashtekar-Streubel phase space,
which is the result of a partial symplectic reduction. The associated momentum
map is the electromagnetic memory in the abelian theory, or a nonlinear,
gauge-equivariant, generalization thereof in the nonabelian case.
  This result follows from an application of Hamiltonian reduction by stages,
enabled by the existence of a natural normal subgroup of the gauge group on a
null codimension-1 submanifold with boundaries. The first stage is coisotropic
reduction of the Gauss constraint, and it yields a symplectic extension of the
Ashtekar-Streubel phase space (up to a covering). Hamiltonian reduction of the
residual gauge action leads to the fully-reduced phase space of the theory.
This is a Poisson manifold, whose symplectic leaves, called superselection
sectors, are labelled by the (gauge classes of the generalized) electric flux
across the boundary.
  In this framework, the Ashtekar-Streubel phase space arises as an
intermediate reduction stage that enforces the superselection of the electric
flux at only one of the two boundary components. These results provide a
natural, purely Hamiltonian, explanation of the existence of soft symmetries as
a byproduct of partial symplectic reduction, as well as a motivation for the
expected decomposition of the quantum Hilbert space of states into irreducible
representations labelled by the Casimirs of the Poisson structure on the
reduced phase space.
