Unstable Particles

Unstable particles cannot be treated as asymptotic external states in $S$-matrix theory and when they occur as resonant states cannot be described by finite-order perturbation theory. The known facts concerning unstable particles are reviewed and it is shown how to construct gauge-invariant expressions for matrix elements containing intermediate unstable particles and physically meaningful production cross-sections for unstable particles. The results and methodology presented are relevant for $Z^0$ resonance physics, $W^+W^-$ and $Z^0Z^0$ pair production and can be straightforwardly applied to other processes.