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 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.
Zúñiga-Galindo, W. A. “Non-Archimedean Statistical Field Theory.” Reviews in Mathematical Physics, Apr. 2022, p. 2250022, https://doi.org/10.1142/S0129055X22500222.
Reviews in Mathematical Physics