Haag’s Theorem—a working physicist’s perspective

The perils of excessive idealization in constructing the underlying mathematical framework for fundamental physical theories are illustrated with some examples taken from relativistic quantum field theory: the triviality issue for standard model field theories, the nonexistence of the S-matrix in quantum electrodynamics, and Haag’s no-go theorem for the interaction picture formulation of relativistic field theories. It is argued that in all cases, known physical limitations of the theory, once taken into account, remove the apparent failure of the formalism, allowing phenomenologically relevant calculations to be made.