In the context of quantum field theory, virtual particles, including virtual photons, are mathematical constructs used to describe interactions between elementary particles. They are considered "virtual" because they do not necessarily correspond to observable, on-shell particles that exist as stable, free particles.
Virtual photons, for example, are exchanged in electromagnetic interactions between charged particles. They mediate the electromagnetic force. However, virtual particles do not have all the properties of real particles. They can violate energy-momentum relations and do not satisfy the mass-shell condition (the equation E² = p²c² + m²c⁴, where E is energy, p is momentum, m is mass, and c is the speed of light).
While virtual particles are not directly observable, their effects can be measured indirectly through their influence on measurable quantities, such as scattering cross-sections or energy levels. They play a crucial role in quantum field theory calculations and are an integral part of understanding and predicting particle interactions.
It's important to note that the term "real" can be somewhat ambiguous in the context of virtual particles. Virtual particles are not persistent, long-lived entities in the same way that observable, on-shell particles are. However, they are considered "real" in the sense that their effects can be observed and measured within the framework of quantum field theory.