The particle Fock space of the matter fields in QED can be constructed usin
g the free creation and annihilation operators. However, these particle ope
rators are not, even at asymptotically large times, the modes of the matter
fields that enter the QED Lagrangian. In this letter we construct the fiel
ds which do recover such particle modes at large times. We are thus able to
demonstrate for the first time that, contrary to statements found in the l
iterature, a relativistic description of charged particles in QED exists. (
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