  We discuss a reformulation of QED in which matter and gauge fields are
integrated out explicitly, resulting in a many-body Lorentz covariant theory of
0+1 dimensional worldlines describing super-pairs of spinning charges
interacting through Lorentz forces. This provides a powerful, string inspired
definition of amplitudes to all loop orders. In particular, one obtains a more
general formulation of Wilson loops and lines, with exponentiated dynamical
fields and spin precession contributions, and worldline contour averages
exactly defined through first quantized path integrals. We discuss in detail
the attractive features of this formalism for high order perturbative
computations. We show that worldline S-matrix elements, to all loop orders in
perturbation theory, can be constructed to be manifestly free of soft
singularities, with infrared (IR) divergences captured and removed by endpoint
photon exchanges at infinity that are equivalent to the soft coherent dressings
of the Dyson S-matrix proposed by Faddeev and Kulish. We discuss these IR
structures and make connections with soft theorems, the Abelian exponentiation
of IR divergences and cusp anomalous dimensions. Follow-up papers will discuss
the efficient computation of cusp anomalous dimensions and universal features
of soft theorems.
