Classical limit of a scalar quantum field theory

It is well known that a minimal distance emerges in quantum field theories owing to the need to regularize the UV divergences. The macroscopical limit at large minimal distance, and weak spatial resolution, is investigated for a self-interacting scalar quantum field theory with the help of the renormalization group. The lowering of the cutoff always opens the dynamics, hence the renormalization group has to be implemented for open quantum field theories. A strongly coupled nonrelativistic scaling regime is found, supporting a second-order phase transition between weakly and strongly open theories. The weakly (strongly) open bare theories develop into strongly (weakly) open dynamics during the renormalization group flow. The two known conditions of the classical limit, the strong decoherence and the suppression of the quantum fluctuations, are confirmed for closed bare theories at distances beyond a nonrelativistic correlation length.