  We propose a mapping between geometry and kinematics that implies the
classical equivalence of any theory of massless bosons -- including spin and
exhibiting arbitrary derivative or potential interactions -- to a nonlinear
sigma model (NLSM) with a momentum-dependent metric in field space. From this
kinematic metric we construct a corresponding kinematic connection, covariant
derivative, and curvature, all of which transform appropriately under general
field redefinitions, even including derivatives. We show explicitly how all
tree-level on-shell scattering amplitudes of massless bosons are equal to those
of the NLSM via the replacement of geometry with kinematics. Lastly, we
describe how the recently introduced geometric soft theorem of the NLSM, which
universally encodes all leading and subleading soft scalar theorems, also
captures the soft photon theorems.
