Non-Archimedean Statistical Field Theory

Abstract

We construct in a rigorous mathematical way interacting quantum field theories on a p-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 calculation of the correlation functions is carried out in the standard form. In the case of $\varphi^{4}$-theories, we show the existence of systems admitting spontaneous symmetry breaking.