The philosophical significance of the concept of superposition in quantum field theory

I analyse the applicability of the concept of superposition within quantum field theory (QFT) in order to consider the physical interpretation of a simple interacting theory. First, I consider the significance of ‘superposition’ in classical physics motivated by the philosophical framework developed by Wilson (2006; 2017), via the analyses of ‘superposition’ developed by Volkmann (1896; 1910) and Simons (1987) in addition to a historical survey of its application with special reference to Fourier techniques. The concept has a patchwork or façade structure, with application subject to ‘prolongation’ and ‘semantic mimicry’. Proper usage of ‘superposition’ is associated with identifying partial states and laws that provide a natural description of complicated phenomena supporting physically salient explanations, inductive inferences and counterfactual reasoning. Secondly, I demonstrate that application of ‘superposition’ in quantum physics is a prolongation of its classical usage involving new rules of application. Thirdly, I analyse the historical origins of QFT and the mature theory to indicate where, and how, proper application of ‘superposition’ is made to free theories, whilst semantic mimicry is involved in the interpretation of interacting theories. Improper and often implicit appeals are made to ‘superposition’ to incorrectly claim physical interpretations of interacting theories. Two major related failures of ‘superposition’ are identified, associated with the initial postulation of putative fields and corresponding states associated with different particle types, and with the nonlinearity of the coupled field equations, so that natural descriptions of interacting states using familiar concepts are unavailable. Renormalization is interpreted as a symptom and pragmatic partial remedy for the failure of ‘superposition’ such that empirically successful calculations are supported using LSZ scattering theory and the Gell-Mann and Low theorem. Finally, I suggest that the interpretation of QFT is best approached within the context of an engineer’s perspective rather than a metaphysician’s, having implications for wider philosophical debates