Haag's theorem asserts that free fields and interacting fields exist in different, unitarily inequivalent Hilbert spaces, meaning a free field cannot transform into an interacting one. The theorem highlights the mathematical ill-definition of transitioning from free to interacting fields due to infrared divergences. While this poses challenges for traditional perturbative methods, alternative approaches like the algebraic framework effectively address these issues. The algebraic approach is designed to handle unitarily inequivalent representations, making Haag's theorem less problematic in that context. Understanding these distinctions is crucial for advancing quantum field theory.