  The nucleon's electromagnetic form factors are expressed in terms of the
transverse densities of charge and magnetization at fixed light-front time. At
peripheral transverse distances $b = O(M_\pi^{-1})$ the densities are governed
by chiral dynamics and can be calculated model-independently using chiral
effective field theory (EFT). We represent the leading-order chiral EFT results
for the peripheral transverse densities as overlap integrals of chiral
light-front wave functions, describing the transition of the initial nucleon to
soft pion-nucleon intermediate states and back. The new representation (a)
explains the parametric order of the peripheral transverse densities; (b)
establishes an inequality between the spin-independent and -dependent
densities; (c) exposes the role of pion orbital angular momentum in chiral
dynamics; (d) reveals a large left-right asymmetry of the current in a
transversely polarized nucleon and suggests a simple interpretation. The
light-front representation enables a first-quantized, quantum-mechanical view
of chiral dynamics that is fully relativistic and exactly equivalent to the
second-quantized, field-theoretical formulation. It relates the charge and
magnetization densities measured in low-energy elastic scattering to the
generalized parton distributions probed in peripheral high-energy scattering
processes. The method can be applied to nucleon form factors of other
operators, e.g. the energy-momentum tensor.
