Part 3/10:
One perspective on the difficulty in defining QFT rigorously springs from examining Quantum Electrodynamics (QED)—the quantum field theory describing the interactions between electrons and photons. In practice, physicists consider incoming and outgoing particle states to compute probabilities of various outcomes, focusing on scattering amplitudes associated with these particles. This approach largely aligns with quantum mechanics axioms, allowing computations to sidestep deeper foundational issues.