Ontological Theory behind Interacting Scalar Quantum Field Theory

We show how one can reproduce the state evolution known from interacting QFT from an ontological deterministic theory. This is an important step in finding the reality that underlies QFT.In previous work ontic theories behind free QFTs were found, for all QFTs that occur in the Standard Model (spin-0, spin-1/2 & spin-1). In this paper we extend the ontological theory behind QFT to the case with interactions. We do this by starting out from the ontic theories found for free QFTs and see what happens if we try to include interactions (known from QFT). This will lead us to the conjecture that the ontic theory behind any QFT with interaction is, at the basis, the corresponding classical field theory. We study such a classical field theory for the case of a real scalar field with φn-interaction. We determine the evolution of the probability density of the ontic fields and cast it into a formalism known from QFT. We will focus on the simplest case of self-interaction, to illustrate our procedure. We find that we can reproduce the probability evolution from real scalar QFT with (self-)interaction, for this simplest case.