Evaluation of functional integrals for an ultralocal static field theory

Exact and perturbative solutions of an ultralocal, static, real φ^m field theory, obtained by functional integral methods are given and discussed. It is shown that this unrenormalizable theory leads to a free one in the local limit, whereas a small non-locality leads to a small effective coupling constant in an effective φ⁴ Lagrangian. It is proved that the usual perturbation seeries is the asymptotic expansion of the exact result.