Virtual photons, which are particle-like entities that mediate the electromagnetic interaction between charged particles, can indeed be associated with two or three polarization states, depending on the context in which they are considered. Let me explain further.
In the case of real or physical photons, which are the quanta of the electromagnetic field, they are known to have two independent polarization states: horizontal (H) and vertical (V), or equivalently, perpendicular electric field components. These two polarization states represent the two transverse directions in which the electric field of the photon can oscillate.
However, when it comes to virtual photons, the situation can be more nuanced. Virtual particles, including virtual photons, exist only within the framework of quantum field theory and are not directly observable. They are mathematical constructs that arise in calculations to describe interactions between charged particles.
In certain quantum field theories, such as quantum electrodynamics (QED), virtual photons are associated with three polarization states. In addition to the horizontal and vertical polarizations (H and V), there is a third polarization state known as longitudinal (L), which corresponds to an electric field component parallel to the direction of motion of the virtual photon.
The presence of the longitudinal polarization state in virtual photons arises from the non-zero mass of the charged particles involved in the interaction. In QED, virtual photons can interact with massive charged particles, and this interaction leads to the emergence of the longitudinal polarization state.
It's important to note that the longitudinal polarization of virtual photons differs from that of real photons. Real photons, being massless particles, do not possess a longitudinal polarization state. This distinction arises because virtual particles are not constrained by the same on-shell conditions (energy-momentum relation) as real particles and can exhibit different properties.
In summary, virtual photons can have three polarization states (H, V, and L) in certain contexts, while physical photons have two polarization states (H and V). The additional longitudinal polarization of virtual photons is a consequence of the interaction between the virtual photon and massive charged particles.