In quantum field theory (QFT), virtual particles are a mathematical construct used in calculations to describe interactions between particles. They are not directly observable entities but are rather a convenient way to represent the exchange of energy and momentum during particle interactions.
In QFT, particles are represented as excitations of underlying fields, such as the electromagnetic field or the electron field. These fields pervade all of space, and particles can be created or annihilated by interacting with these fields. When particles interact, they exchange virtual particles, which are considered off-shell, meaning they do not obey the usual mass-energy relationship for on-shell particles.
Virtual particles are used in Feynman diagrams, which are pictorial representations of particle interactions. Feynman diagrams illustrate the various possible processes that can occur during a particle interaction, and virtual particles appear as internal lines connecting the incoming and outgoing particles. Each line represents a propagator, which describes the probability amplitude for a particle to travel from one point to another.
The exchange of virtual particles in Feynman diagrams allows us to calculate the probability amplitudes and cross-sections for particle interactions. The calculations involve summing over all possible paths and interactions, including the contributions from virtual particles. These calculations take into account the conservation of energy and momentum at each vertex in the Feynman diagram.
Although virtual particles are not directly detectable, their effects can be observed through their influence on measurable quantities. For example, the interaction between charged particles can be described by the exchange of virtual photons, which leads to the observed electromagnetic forces.
It's worth noting that virtual particles should not be interpreted as particles popping in and out of existence in the literal sense. They are a mathematical tool used to facilitate calculations within the framework of quantum field theory and provide a way to account for the exchange of energy and momentum during particle interactions.