Massless Particles

Here we study the internal space-time symmetries of massless particles, among which photons are particularly significant due to their involvement in the development of quantum mechanics and in quantum electrodynamics, which deals with the interaction of photons with charged particles. One of the difficulties associated with studying photons has been that the four-vector form for the photon wave function is not unique, depending on gauge degrees of freedom which are not measurable. The little group for massless particles is E(2)-like. A closer look at matrices of the E(2)-like group applicable to the photon four-vector indicates that they form a finite-dimensional non-unitary representation. We associate rotations of the E(2)-like group with the helicity and the translation-like transformations with gauge degrees of freedom. The four-momentum of relativistic particles is altered by Lorentz transformations, whose rotations are represented by unitary matrices, while boosts by non-unitary matrices. Therefore, we consider the possibility of constructing a unitary representation by combining the boost and gauge transformations.