THE O(N) GROSS-NEVEU AND SUPERSYMMETRIC σ MODELS ON p-ADIC FIELDS

Abstract

We construct a fermion kinetic operator for fields over the p-adic number fields, Qp, and find p must be restricted to certain values to have correct fermion statistics. It is used to formulate the O(N) Gross-Neveu model and to consider the supersymmetric O(N)σ model on p-adic fields. We show that within the large N expansion they have the same vacuum structure as their real counterparts.