Regge behaviour and Regge trajectory for ladder graphs in scalar $\Phi^3$ field theory

Abstract

Using the gaussian representation for propagators (which can be proved to be exact in the infinite number of loops limit) we are able to derive the Regge behaviour for ladder graphs of $\phi^3$ field theory in a completely new way. An analytic expression for the Regge trajectory $\alpha (t/m^2)$ is found in terms of the mean-values of the Feynman $\alpha$-parameters. $\alpha (t/m^2)$ is calculated in the range $- 3.6 < t/m^2 < 0.8$. The intercept $\alpha (0)$ agrees with that obtained from earlier calculations using the Bethe-Salpeter approach for $\alpha (0) \gsim 0.3$.