A phase cell cluster expansion for a hierarchical 34 model

The formalism developed in a previous paper is applied to yield a phase cell cluster expansion for a hierarchical 34 model. The field is expanded into modes with specific renormalization group scaling properties. The present cluster expansion for a vacuum expectation value is formally the natural factorization of each term in the perturbation expansion into the contribution of modes connected to the variables in the expectation via interactions, and that of the complementary set. The expectation value is thus realized as a sum of contributions due to finite subsets of the modes. We emphasize the following additional features: 1) Partitions of unity are not used. 2) There are essentially no cut-offs. 3) The expansion is developed directly, without an initial need to prove an ultraviolet stability bound, the most difficult part of the traditional approach. Our main interest in the present phase cell cluster expansion is founded in the belief that it may be the right vehicle for proving the existence of a nontrivial four-dimensional field theory. 1983 Springer-Verlag.

A phase cell cluster expansion for a hierarchical 34 model Academic Article