This has been discussed on a number of recent threads but, because of the Feynman QED reference, perhaps a further explanation is appropriate. We can OBSERVE photons (and other "particles") as waves or as particles .
This depends on the kind of experiment we do; if the experiment depends on the momentum of the photon, then it can be interpreted as a particle with momentum and energy. If it is an interference type experiment, like the famous double slit, then it is usually interpreted as a wave phenomenon.
But Feynman saw a way to explain the slit experiment with a particle interpretation. He theorized that the particle has an amplitude which is a complex number (he never calls it that, but if you follow his rules for adding and multiplying his "little arrows", that is what they boil down to). The particle follows all possible paths in the experiment and you add up the amplitudes over the paths and most of them cancel each other out, and Presto! the interference comes out.
This does not mean Feynman denied the wave interpretation or said that only a particle interpretation is necessary. His book is, after all, a description of the QED field theory, in which fields are the primary constituents, and particles in any guise are just quanta, bundles of field energy that come and go.