Non-Archimedean statistical field theory

Abstract

We construct in a rigorous mathematical way interacting quantum field theories on a [Formula: see text]-adic spacetime. The main result is the construction of a measure on a function space which allows a rigorous definition of the partition function. The advantage of the approach presented here is that all the perturbation calculations can be carried out in the standard way using functional derivatives, but in a mathematically rigorous way.