Quantum Field Theory: Underdetermination, Inconsistency, and Idealization

Quantum field theory (QFT) presents a genuine example of the underdetermination of theory by empirical evidence. There are variants of QFT which are empirically indistinguishable yet support different interpretations. This case is of particular interest to philosophers of physics because, before the philosophical work of interpreting QFT can proceed, the question of which variant should be subject to interpretation must be settled. At one end of the spectrum of variants of QFT is the version which is found in introductory textbooks and employed by most working physicists; this is the variant of QFT which introduces renormalization procedures to facilitate the calculation of scattering matrix elements. At the other end of the spectrum are axiomatic presentations of QFT, which are rigorous but remote from practical applications. New arguments are offered for basing the interpretation of QFT on a rigorous axiomatic variant of the theory. The pivotal considerations are the roles that consistency and idealization play in this case.