Yes, it would be correct to say that "virtual" particles exist in theoretical mathematics but have not been observed directly in experiments. Virtual particles are a concept within quantum field theory used as a mathematical tool to calculate the behavior of interacting quantum fields.
In quantum field theory, the vacuum is not an empty void but is rather a seething sea of virtual particles and their corresponding antiparticles spontaneously appearing and annihilating in a short time. These virtual particles arise due to the uncertainty principle, which allows for temporary violations of energy conservation as long as they are within the time-energy uncertainty relation. They are considered "virtual" because they do not correspond to particles that can be directly detected or measured with physical instruments.
Virtual particles play a crucial role in calculations of particle interactions and processes within quantum field theory. For example, they contribute to the formulation of Feynman diagrams, which are graphical representations used to calculate the probabilities of different particle interactions. Virtual particles appear as intermediate lines in these diagrams, mediating interactions between incoming and outgoing particles.
While virtual particles are a useful mathematical tool in quantum field theory, they are not directly observed in experiments. This is because their existence is tied to the mathematical formalism and calculations used to describe particle interactions. However, their effects can be indirectly observed or inferred through their measurable consequences, such as shifts in energy levels, modifications of scattering patterns, or the Lamb shift in atomic spectra.
It's worth noting that the term "virtual particles" is a convenient way of describing mathematical entities within the framework of quantum field theory. The underlying reality behind these mathematical constructs and their interpretation is an ongoing subject of debate and discussion among physicists.