Dressed photons from the viewpoint of photon localization: the entrance to the off-shell science

Abstract

In the present paper, a new aspect of the interplay is examined between mathematical–physical arguments and light–matter fusion technologies in terms of the concept of “effective mass”, starting from a question: Who has seen a free photon? Owing to the general results due to Newton–Wigner and to Wightman, a position operator is absent for massless free particles with non-zero finite spins, and hence, we cannot observe free photons in any local space regions. To solve this paradox of “photon localization”, the effective mass of a photon needs to be generated through the couplings of photons with matter. Here “polaritons” picture as a basic notion in optical and solid physics is shown to verify this viewpoint, which is seen to apply also to more general settings . Focusing on the role played by nanoparticles, we reach a new look at the notion of “dressed photons” as off-shell particles. The perspective above shows that essential mathematical structure of quantum field theory for the so-called elementary particles in subatomic scale can also be applied to certain phenomena in the nano-scale.