Regge trajectories in the phi3 multiperipheral model with strong coupling

The trajectory function α(t) for small t is studied in the φ³ multiperipheral model as the coupling constant becomes very large. Special emphasis is paid to the analogy of the φ³ model to a one-dimensional gas system. We discuss the upper and lower bounds for α(t) when 2,3,... up to N-body potentials in the gas model are taken into account. The power dependence of α on the coupling constant as well as its dependence on N is determined by our bounds. This power dependence changes as N approaches infinity; it also changes as the mass ratio of the produced final particles to the exchanged particles varies. We show that the equal-spacing approximation suggested by T. D. Lee gives the correct power dependence of α on the coupling constant with a coefficient in error by only a few percent.