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 reasonablehypotheses and the central limit theorem of mathematical statistics,that a large class of scalar field models in quantum field theory aretrivial, in the sense that all their expectation values can be obtainedfrom related purely Gaussian models. This implies that there are nointer-particle interactions in most of these models, with a singleexception, and therefore that under quantization they reduce to theoriesof free particles, a situation known as the triviality of the models.