A Feynman diagram is a graphical representation of terms in a perturbative quantum-field-theory calculation. External lines represent incoming and outgoing particles, vertices represent interaction terms, and internal lines correspond to propagators summed or integrated over unobserved intermediate degrees of freedom.

For electron-muon scattering, $$e^-+\mu^-\rightarrow e^-+\mu^-,$$ a lowest-order electromagnetic diagram contains an electron line and a muon line connected by an internal photon line. The diagram encodes a mathematical amplitude built from electromagnetic vertices and a photon propagator.

A diagram should not be read as a literal microscopic movie in which particles follow drawn trajectories or a detectable 'virtual photon' travels between them. Internal lines are parts of an integral contributing to a quantum amplitude and generally do not satisfy the same on-shell energy-momentum relation as observable particles.

Different diagrams leading to the same external state contribute amplitudes that must be added before taking the squared magnitude. Their interference can therefore strengthen or suppress probabilities.

The usefulness of diagrams is organizational. As perturbative order increases, they enumerate allowed contributions while preserving conservation rules at vertices. They also make crossing relationships and interaction structure visually apparent.

Feynman diagrams connect the qualitative language of 'particles interacting' to actual quantum-field calculations, but the diagram is notation for mathematics rather than an independent physical mechanism.