Perturbative expansions and the foundations of quantum field theory.

Perturbative expansions have played a peculiarly central role in quantum field theory, not only in extracting empirical predictions but also in investigations of the theory's mathematical and conceptual foundations. This paper brings the special status of QFT perturbative expansions into focus by tracing the history of mathematical physics work on perturbative QFT and situating a contemporary approach, perturbative algebraic QFT, within this historical context. Highlighting the role that perturbative expansions have played in foundational investigations helps to clarify the relationships between the formulations of QFT developed in mathematical physics and high-energy phenomenology. [ABSTRACT FROM AUTHOR]