Regge Trajectory in Field Theory

The form of the Regge trajectory, the graph of the complex angular momentum $\alpha \mathrm{}\left(t\right)\mathrm{}$ as a functions of the square of the momentum transfer $t$, is studied in field theory within the framework of the ladder approximation in the crossed channel. To order $g^2$, the trajectory is unbounded in the region $t\approx 4m^2$, but inclusion of the higher-order terms in $g^2$ removes the divergence and leads to a smooth trajectory that resembles that expected from potential scattering. The various relations between $g^2$, $\alpha \mathrm{}\left(t\right)\mathrm{}$, and the exchanged mass are discussed.