Feynman proposed the idea that every antiparticle could mathematically be considered a normal particle moving backwards in time. An annihilation between a particle or its antiparticle would be a time-reversal event for a single particle.
Feynman later disregarded this hypothesis, as it predicted that antimatter should possess negative mass. If this were true, energy could be conserved and no photons or other particles would be created. Experiments have refuted this prediction.
Feynman diagrams still represent an antiparticle in the form of a backward-directed, arrow. This is a remnant of his early hypothesis. The original meaning of the symbols is still valid, but they are not used anymore.