In quantum field theory (QFT), the terms "particle" and "virtual particle" have specific meanings. Let's start with the formal mathematical definitions of these terms.
- Particle: In QFT, a particle is described as a state of the corresponding quantum field that satisfies the field's equations of motion, such as the Klein-Gordon equation or the Dirac equation. A particle is associated with a specific set of quantum numbers, including its mass, spin, and charge. Mathematically, a particle state is represented as a one-particle state vector in the Fock space of the theory.
In the context of perturbation theory, particle states are often described in terms of asymptotic in and out states. These states are associated with free particle solutions of the field equations that represent particles far in the past (incoming states) or far in the future (outgoing states). The asymptotic in and out states serve as a convenient basis for calculating scattering amplitudes.
- Virtual Particle: In QFT, virtual particles are not directly observable particles but rather intermediate states that appear in Feynman diagrams during perturbative calculations. They are called "virtual" because they do not correspond to particles propagating on-shell (i.e., following their classical equations of motion). Instead, they are associated with off-shell states, which do not satisfy the on-shell conditions for mass and energy.
Mathematically, virtual particles are represented as propagators or internal lines in Feynman diagrams. These lines do not correspond to real particles that can be directly detected but are rather a mathematical tool used to compute probabilities for particle interactions. The internal lines can be associated with virtual particles that are created and annihilated within very short timescales dictated by the uncertainty principle.
It's important to note that virtual particles do not have the same physical properties as real particles. For example, they can have masses different from the physical mass of the corresponding particle and may violate energy-momentum conservation. However, their effects can be incorporated into the calculations, leading to predictions that agree with experimental observations.
In summary, particles in QFT are described by quantum field states satisfying the field equations, while virtual particles are intermediate states that appear in Feynman diagrams during perturbative calculations, representing off-shell processes that are not directly observable.