  The low-energy effective field theory is constructed by integrating out
Standard Model states with masses proximate to the electroweak scale. We report
the equations of motion for this theory, including corrections due to higher
dimensional operators up to mass dimension six. We construct the corresponding
symmetry currents, and discuss how the $\rm SU(2)_L \times U(1)_{\mathsf{y}}$
symmetry, and global symmetries, are manifested when Standard Model states are
integrated out. Including contributions from higher dimensional operators to
the equations of motion modifies the interpretation of conserved currents. We
discuss the corrections to the electromagnetic current as an example, showing
how modifications to the equation of motion, and corresponding surface terms,
have a direct interpretation in terms of multipole charge distributions that
act to source gauge fields.
