The functional renormalization group flow of a scalar field theory with quartic couplings and sharp spatial momentum cutoff is presented in four-dimensional Minkowski space-time for the bare action by retaining entanglement IR UV particle modes. It argued that open interaction channels have to be taken into account quantum defined help cutoff, non-perturbative UV-IR found closed or almost models.

Introduction/purpose: The principal techniques of regularization schemes and their validity for gauge field theories are discussed. Methods: Schemes dimensional regularization, Pauli-Villars lattice Results: Coleman-Mandula theorem shows which renormalizable. Conclusion: Some renormalizable, the Standard Model in particular.