In quantum field theory divergent expressions are "discarded", leaving finite expressions which provide the best predictions anywhere in science. In fact, this "renormalization procedure" involves no mystery or illegitimate operations. This paper explains, in terms accessible to non-experts, how the procedure really works and explores some different ways in which physicists have suggested that one understand it.

This paper digests technical commonplaces of quantum field theory to present an informal interpretation of the theory by emphasizing its connections with the harmonic oscillator. The resulting "harmonic oscillator interpretation" enables newcomers to the subject to get some intuitive feel for the theory. The interpretation clarifies how the theory relates to observation and to quantum mechanical problems connected with observation. Finally the interpretation moves some way towards helping us see what the theory comes to physically. The paper also argues that, (...) in important respects, interpretive problems of quantum field theory are problems we know well from conventional quantum mechanics. An important exception concerns extending the puzzles surrounding the superposition of properties in conventional quantum mechanics to an exactly parallel notion of superposition of particles. Conventional quantum mechanics seems incompatible with a classical notion of property on which all quantities always have definite values. Quantum field theory presents an exactly analogous problem with saying that the number of "particles" is always definite. (shrink)

Since 1980 effective field theories (EFT's) have been the focus of much research by quantum field theorists but their philosophical implications have gone mostly unnoticed. Some authors claim EFT's are approximations to some fundamental theory. Others claim EFT's are ends in themselves, not approximations to some fundamental theory, and that we can use them to bypass the problem of renormalization. In the present work I argue that the EFT programme can bypass the problem if ontological commitments only come from theoretical (...) predictions. Since the history of QFT suggests some form of entity realism, the EFT programme does not allow us to bypass the problem of renormalization. (shrink)