I give a brief introduction to how Feynman diagrams are used. I review arguments to the effect that they are only used as calculation tools and should not be interpreted as representations of physical processes. Against these arguments, I propose to regard Feynman diagrams as visual models that explain, in some respects, how elementary particles interact.

I argue against the currently prevalent view that algebraic quantum field theory (AQFT) is the correct framework for philosophy of quantum field theory and that “conventional” quantum field theory (CQFT), of the sort used in mainstream particle physics, is not suitable for foundational study. In doing so, I defend that position that AQFT and CQFT should be understood as rival programs to resolve the mathematical and physical pathologies of renormalization theory, and that CQFT has succeeded in this task and AQFT (...) has failed. I also defend CQFT from recent criticisms made by Doreen Fraser. (shrink)

I analyse the conceptual and mathematical foundations of Lagrangian quantum field theory (QFT) (that is, the ‘naive’ (QFT) used in mainstream physics, as opposed to algebraic quantum field theory). The objective is to see whether Lagrangian (QFT) has a sufficiently firm conceptual and mathematical basis to be a legitimate object of foundational study, or whether it is too ill-defined. The analysis covers renormalisation and infinities, inequivalent representations, and the concept of localised states; the conclusion is that Lagrangian QFT (at least (...) as described here) is a perfectly respectable physical theory, albeit somewhat different in certain respects from most of those studied in foundational work. (shrink)

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.

It is proposed that we use the term “approximation” for inexact description of a target system and “idealization” for another system whose properties also provide an inexact description of the target system. Since systems generated by a limiting process can often have quite unexpected, even inconsistent properties, familiar limit systems used in statistical physics can fail to provide idealizations, but are merely approximations. A dominance argument suggests that the limiting idealizations of statistical physics should be demoted to approximations.

Haag's theorem has been interpreted as establishing that quantum field theory cannot consistently represent interacting fields. Earman and Fraser have clarified how it is possible to give mathematically consistent calculations in scattering theory despite the theorem. However, their analysis does not fully address the worry raised by the result. In particular, I argue that their approach fails to be a complete explanation of why Haag's theorem does not undermine claims about the empirical adequacy of particular quantum field theories. I then (...) show that such empirical adequacy claims are protected from Haag's result by the techniques that are required to obtain theoretical predictions for realistic experimental observables. I conclude by showing how Haag's theorem is illustrative of a general tension between the foundational significance of results that can be obtained in perturbation theory and non-perturbative characterizations of the content of quantum field theory. (shrink)

There are two distinct interpretations of the role that Feynman diagrams play in physics: (i) they are calculational devices, a type of notation designed to keep track of complicated mathematical expressions; and (ii) they are representational devices, a type of picture. I argue that Feynman diagrams not only have a calculational function but also represent: they are in some sense pictures. I defend my view through addressing two objections and in so doing I offer an account of representation that explains (...) why Feynman diagrams represent. The account that I advocate is a version of that defended by Kendall Walton, which provides us with a basic characterization of the way that representations in general work and is particularly useful for understanding distinctively pictorial representations - in Walton's terms, depictions. The question of the epistemic function of Feynman diagrams as pictorial representations is left for another time. (shrink)

The renormalization group has been characterized as merely a coarse-graining procedure that does not illuminate the microscopic content of quantum field theory but merely gets us from that content, as given by axiomatic QFT, to macroscopic predictions. I argue that in the constructive field theory tradition, RG techniques do illuminate the microscopic dynamics of a QFT, which are not automatically given by axiomatic QFT. RG techniques in constructive field theory are also rigorous, so one cannot object to their foundational import (...) on grounds of lack of rigor. (shrink)

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. (shrink)

Quantum field theory (QFT) presents a genuine example of the underdetermination of theory by empirical evidence. There are variants of QFT—for example, the standard textbook formulation and the rigorous axiomatic formulation—that 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. 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. *Received June 2009; revised August 2009. †To contact the author, please write to: Department of Philosophy, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada; e‐mail: [email protected]. (shrink)

Further arguments are offered in defence of the position that the variant of quantum field theory (QFT) that should be subject to interpretation and foundational analysis is axiomatic quantum field theory. I argue that the successful application of renormalization group (RG) methods within alternative formulations of QFT illuminates the empirical content of QFT, but not the theoretical content. RG methods corroborate the point of view that QFT is a case of the underdetermination of theory by empirical evidence. I also urge (...) caution in extrapolating interpretive conclusions about QFT from the application of RG methods in other contexts (e.g., condensed matter physics). This paper replies to criticisms advanced by David Wallace, but aims to be self-contained. (shrink)

Although the philosophical literature on the foundations of quantum field theory recognizes the importance of Haag’s theorem, it does not provide a clear discussion of the meaning of this theorem. The goal of this paper is to make up for this deficit. In particular, it aims to set out the implications of Haag’s theorem for scattering theory, the interaction picture, the use of non-Fock representations in describing interacting fields, and the choice among the plethora of the unitarily inequivalent representations of (...) the canonical commutation relations for free and interacting fields. (shrink)

Are the generalizations of classical equilibrium thermodynamics true of self-gravitating systems? This question has not been addressed from a foundational perspective, but here I tackle it through a study of the “paradoxes” commonly said to afflict such systems. My goals are twofold: (a) to show that the “paradoxes” raise many questions rarely discussed in the philosophical foundations literature, and (b) to counter the idea that these “paradoxes” spell the end for gravitational equilibrium thermodynamics.

The renormalization group has been characterized as merely a coarse-graining procedure that does not illuminate the microscopic content of quantum field theory, but merely gets us from that content, as given by axiomatic QFT, to macroscopic predictions. I argue that in the constructive field theory tradition, RG techniques do illuminate the microscopic dynamics of a QFT, which are not automatically given by axiomatic QFT. RG techniques in constructive field theory are also rigorous, so one cannot object to their foundational import (...) on grounds of lack of rigor. (shrink)

Quantum field theory, one of the most rapidly developing areas of contemporary physics, is full of problems of great theoretical and philosophical interest. This collection of essays is the first systematic exploration of the nature and implications of quantum field theory. The contributors discuss quantum field theory from a wide variety of standpoints, exploring in detail its mathematical structure and metaphysical and methodological implications.

An Introduction to Quantum Field Theory is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the (...) stage for a discussion of the physical principles that underlie the fundamental interactions of elementary particle physics and their description by gauge field theories. (shrink)

Quantum mechanics is a subject that has captured the imagination of a surprisingly broad range of thinkers, including many philosophers of science. Quantum field theory, however, is a subject that has been discussed mostly by physicists. This is the first book to present quantum field theory in a manner that makes it accessible to philosophers. Because it presents a lucid view of the theory and debates that surround the theory, An Interpretive Introduction to Quantum Field Theory will interest students of (...) physics as well as students of philosophy. -/- Paul Teller presents the basic ideas of quantum field theory in a way that is understandable to readers who are familiar with non-relativistic quantum mechanics. He provides information about the physics of the theory without calculational detail, and he enlightens readers on how to think about the theory physically. Along the way, he dismantles some popular myths and clarifies the novel ways in which quantum field theory is both a theory about fields and about particles. His goal is to raise questions about the philosophical implications of the theory and to offer some tentative interpretive views of his own. This provocative and thoughtful book challenges philosophers to extend their thinking beyond the realm of quantum mechanics and it challenges physicists to consider the philosophical issues that their explorations have encouraged. (shrink)

Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of operator algebras, category theory, etc.. Given the rigor and generality of AQFT, it is a particularly apt tool for studying the foundations of QFT. This paper is a survey of AQFT, with an orientation towards foundational topics. In addition to covering the basics of the theory, (...) we discuss issues related to nonlocality, the particle concept, the field concept, and inequivalent representations. We also provide a detailed account of the analysis of superselection rules by Doplicher, Haag, and Roberts (DHR); and we give an alternative proof of Doplicher and Robert's reconstruction of fields and gauge group from the category of physical representations of the observable algebra. The latter is based on unpublished ideas due to J. E. Roberts and the abstract duality theorem for symmetric tensor *-categories, a self-contained proof of which is given in the appendix. (shrink)