In Quantum Field Theory (QFT), 4-momentum conservation arises from the symmetries of spacetime, specifically through Noether's theorem, which links symmetries to conservation laws. The Hamiltonian formalism provides a framework to derive this conservation, emphasizing that the invariance of the system under time translations leads to energy conservation, while spatial translations lead to momentum conservation. The discussion also touches on the relationship between the golden rule and conservation principles, although the primary focus remains on fundamental symmetries. In classical physics, 4-momentum conservation is similarly derived from these symmetries, reinforcing the connection between classical and quantum frameworks. Understanding these principles is crucial for comprehending the underlying mechanics of both QFT and classical physics.