In this paper we give a general procedure for the construction of the physical states in the case of intercept α(0) = 1. This procedure exhibits in an explicit form the "bootstrap" requirement that the spectrum of the intermediate states, obtained by the factorization of the scattering amplitude, is independent from the particular process used for constructing it. A big advantage of this way is that one avoids the unnecessary introduction of spurious states. The physical states are constructed together with their corresponding operators; this makes it then possible to get scattering amplitudes with the physical states on the external legs. Using the vertex operator associated with the photon-like particle of the level α( s) = 1, we can construct an infinite number of orthogonal and positive norm states, growing up exponentially as the partition function of n objects with only two Lorentz components. The zero mass of the "photon" has been also used to construct operators which transform a physical state belonging to a certain multiplet α( s) = n into another physical state contained in the same multiplet. These operators should be intimately related to the degeneracy of the multiplets. An interesting by-product of this approach is the universality of the "electric charge" and the "magnetic moment."