A particle of mass M and spin J is said to ‘reggeize’ if the amplitude, A, for a process involving the exchange in the t-channel of the quantum numbers of that particle behaves asymptotically in s as

A ∝ sα(t)

where α(t) is the trajectory and α(M2) = J, so that the particle itself lies on the trajectory.

The idea that particles should reggeize has a long history. It was first proposed by Gell-Mann et al. (1962, 1964a,b) and by Polkinghorne (1964). Mandelstam (1965) gave general conditions for reggeization to occur and this was developed by several authors (Abers & Teplitz (1967), Abers et al. (1970), Dicus & Teplitz (1971), Grisaru, Schnitzer, & Tsao (1973)). Calculations in Quantum Electrodynamics (QED) were carried out by Frolov, Gribov & Lipatov (1970, 1971) and by Cheng & Wu (1965, 1969a–c, 1970a,b), who showed that the photon had a fixed cut singularity (as opposed to a Regge pole). On the other hand McCoy & Wu (1976a–f) established that the fermion does indeed reggeize in QED. This was extended to non-abelian gauge theories by Mason (1976a,b) and Sen (1983). The demonstration of reggeization of the gluon was first shown to two-loop order by Tyburski (1976), Frankfurt & Sherman (1976), and Lipatov (1976) and to three loops by Cheng & Lo (1976). The reggeization to all orders in perturbation theory has been established by several authors using somewhat different techniques.