In quantum field theory (QFT), virtual particles are a mathematical concept that arises from the mathematical framework used to describe the behavior of particles and fields. QFT is a theoretical framework that combines quantum mechanics with special relativity and provides a way to describe the behavior of elementary particles and their interactions.
In QFT, particles are described as excitations or quantized vibrations of underlying quantum fields that permeate space. These fields are represented mathematically as operators that satisfy specific equations, such as the Klein-Gordon equation or the Dirac equation.
The mathematical structure of QFT incorporates the concept of particle propagation through the exchange of virtual particles. According to the principles of QFT, particles interact with each other by exchanging virtual particles.
Virtual particles are not the same as real particles that are directly detectable. They are often referred to as "off-shell" particles because they do not satisfy the energy-momentum relation of on-shell particles (particles that are in their mass-energy eigenstates). Virtual particles can be thought of as transient fluctuations or disturbances in the underlying fields that arise during particle interactions.
The presence of virtual particles is mathematically represented through Feynman diagrams, which are graphical tools used in QFT to calculate the probability amplitudes of particle interactions. In Feynman diagrams, real particles are represented as lines, and virtual particles are represented as internal lines connecting the interacting particles.
The Feynman diagrams allow us to calculate the probability amplitudes by summing over all possible virtual particle exchanges. These exchanges contribute to the overall behavior and interaction strengths between particles. However, it's important to note that virtual particles do not have the same physical properties as real particles. They are not directly observable and cannot be detected as individual entities.
The mathematical framework of QFT provides a systematic way to incorporate virtual particles into the description of particle interactions. By considering these virtual particles and their exchanges, QFT allows us to make predictions about observable phenomena and successfully describes a wide range of particle interactions observed in experiments.
It's worth emphasizing that the concept of virtual particles is a mathematical tool and an interpretation of the underlying mathematics of QFT. The actual physical interpretation of these mathematical entities is subject to ongoing debates and interpretations in the field of quantum physics.