A Simple Physical Proof of the Triviality of a Large Class of Scalar Field Models in Euclidean Lattice Quantum Field Theory

We present a mathematical proof, based on a few physically reasonable hypotheses and the central limit theorem of mathematical statistics, that a large class of scalar field models in lattice quantum field theory are trivial in the continuum limit, in three or more spacetime dimensions, in the sense that all their expectation values can be obtained from related purely Gaussian models. This then implies that in the continuum limit there are no inter-particle interactions in these models, and therefore that under quantization they all reduce to theories of free particles, a situation known as the triviality of the models. It should be noted that the triviality argument presented here is completely independent of the representation of lattice quantum field theories by ensembles of random walks, which seems to be the representation used in most triviality-related arguments.