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We discuss a reformulation of QED in which matter and gauge fields areintegrated out explicitly, resulting in a many-body Lorentz covariant theory of0+1 dimensional worldlines describing super-pairs of spinning chargesinteracting through Lorentz forces. This provides a powerful, string inspireddefinition of amplitudes to all loop orders. In particular, one obtains a moregeneral formulation of Wilson loops and lines, with exponentiated dynamicalfields and spin precession contributions, and worldline contour averagesexactly defined through first quantized path integrals. We discuss in detailthe attractive features of this formalism for high order perturbativecomputations. We show that worldline S-matrix elements, to all loop orders inperturbation theory, can be constructed to be manifestly free of softsingularities, with infrared (IR) divergences captured and removed by endpointphoton exchanges at infinity that are equivalent to the soft coherent dressingsof the Dyson S-matrix proposed by Faddeev and Kulish. We discuss these IRstructures and make connections with soft theorems, the Abelian exponentiationof IR divergences and cusp anomalous dimensions. Follow-up papers will discussthe efficient computation of cusp anomalous dimensions and universal featuresof soft theorems.

QED as a many-body theory of worldlines: I. General formalism and infrared structure