The renormalisation group and effective field theories

Much apprehension has been expressed by philosophers about the method of renormalisation in quantum field theory, as it apparently requires illegitimate procedure of infinite cancellation. This has lead to various speculations, in particular in Teller (1989). We examine Teller's discussion of perturbative renormalisation of quantum fields, and show why it is inadequate. To really approach the matter one needs to understand the ideas and results of the renormalisation group, so we give a simple but comprehensive account of this topic. With this in hand, we explain how renormalisation can and should be understood. One thing that is revealed is that apparently very successful theories such as quantum electro-dynamics cannot be universally true; resolving the tension between success and falsity leads to a picture in which any theory may be viewed as irreducibly phenomenological. We explain how, and argue that the support for this view is tenuous at best.We are very grateful to Stephen Shenker in his patient efforts to help us understand this material, and to the helpful comments of Paul Teller and two anonymous referees. Some of the ideas presented here are based on material in the Ph.D. thesis of one of us (Huggett) submitted to Rutgers University.     

On the field aspect of Quantum fields

In this paper we contrast the idea of a field as a system with an infinite number of degrees of freedom with a recent alternative proposed by Paul Teller in Teller (1990). We show that, although our characterisation lacks the immediate appeal of Teller's, it has more success producing agreement with intuitive categorisations than his does. We go on to extend the distinction to Quantum Mechanics, explaining the important role that it plays there. Finally, we take some time to investigate the way in which strings are to be considered fields, and the important differences with scalar fields. Overall, we aim to show that many types of systems may be viewed as fields, and to point out significant distinctions amongst them, thereby expanding our understanding of what it is to fall in this category.Thanks to our anonymous referees for invaluable comments.     

Why manifold substantivalism is probably not a consequence of classical mechanics

This paper develops and defends three related forms of relationism about spacetime against attacks by contemporary substantivalists. It clarifies Newton's globes argument to show that it does not bear on relations that fail to determine geodesic motions, since the inertial effects on which Newton relies are not simply correlated with affine structure, but must be understood in dynamical terms. It develops remarks by Sklar and van Fraassen into relational versions of Newtonian mechanics, and argues that Earman does not show them to trivialize the debate.