Virtual particle

A virtual particle is an internal excitation in a perturbative quantum-field calculation, represented by an internal line in a Feynman diagram. It is generally not directly observable and need not satisfy the energy–momentum relation of a real particle.

Feynman diagram: A graphical representation of terms in a perturbative quantum-field calculation, with lines and vertices encoding mathematical factors. Its internal lines represent virtual-particle propagators.
On-shell particle: A particle state whose energy and momentum satisfy the relativistic mass-shell relation. Virtual particles can be off shell, unlike freely propagating real particle states.
Quantum field theory: A framework describing particles and their interactions through quantized fields that can create and annihilate excitations. Virtual particles belong to its perturbative descriptions of interactions.
Lamb shift: A small difference between hydrogen energy levels predicted to be degenerate by the Dirac equation. Quantum-electrodynamic corrections, often illustrated with virtual-photon diagrams, account for it.
Propagator: A mathematical function describing how a field's disturbance contributes between two spacetime points or interaction vertices. Each internal line contributes a propagator to the diagram's amplitude.
Off-shell particle: An internal or intermediate particle-like contribution whose four-momentum does not satisfy the mass-shell relation. This is the kinematic sense commonly associated with virtual particles.
Quantum field: A physical field whose excitations are described by quantum mechanics and interpreted as particle states. Virtual-particle lines encode contributions from field excitations.
Casimir effect: An attraction or repulsion between material boundaries arising from changes in quantum-field vacuum energy. Virtual-particle imagery is common, though the effect is more precisely derived from field fluctuations and boundary conditions.
Feynman rules: Rules that translate a quantum-field theory's diagrams into mathematical expressions for scattering amplitudes. They specify the factors assigned to virtual-particle lines and vertices.
Asymptotic state: A quantum state describing particles sufficiently far before or after an interaction to be treated as free. Virtual particles are internal calculation elements, not the incoming or outgoing states.

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