Expansion Of Phase Space Research Articles

Asymptotic completeness and multiparticle structure in field theories

The ideas developed in Part I (ref. (1)) are applied to the recently constructed massive Gross-Neveu model. We define in this case an irreducible kernel satisfying a regularized Bethe-Salpeter equation which is convenient to derive asymptotic completeness in the 2-particle region. As in Part I, the method aIlows direct graphical definition of general irreducible kernels and is well suited to the analysis of asymptotic completeness and related results in more general energy regions. A large part of the paper is devoted to a new self-contained construction (via phase space expansion) of the Gross-Neveu model. The presentation is somewhat simpler than previous ones, is more complete on some points and is best suited to our purposes.

The Lipatov argument for ? 3 4 perturbation theory

We extend toϕ 3 4 the work of S. Breen on the leading behavior at large order ofϕ 2 4 perturbation theory. Using a phase space expansion to obtain new estimates on the high energy behavior ofϕ 3 4 Feynman graphs, and a rigorous semiclassical expansion, we prove that the radius of convergence of the Borel transform of the pertubative series forϕ 3 4 Euclidean field theory is the one computed by the Lipatov method.