Almost zero-dimensional quantum field theories

A new approach is proposed for obtaining nonperturbative information from a quantum field theory using an analytic (non-numerical) procedure. The idea is to expand the Green’s functions of the quantum field theory as series in powers of D, the space-time dimension. The leading term in such an expansion is easy to calculate because it requires that we solve the corresponding zero-dimensional field theory. In this paper we develop a strategy for computing the coefficients of higher powers of D. The D expansion appears to have a finite radius of convergence. Initial numerical studies suggest that only a small number of terms in the D expansion are required to obtain accurate results.