# Philosophy of Quantum Field Theory

### Naturalness and Emergence (2019)

*The Monist* 102 (2019) pp.499-524.

I develop an account of naturalness (that is, approximately: lack of extreme fine-tuning) in physics which demonstrates that naturalness assumptions are not restricted to narrow cases in high-energy physics but are a ubiquitous part of how interlevel relations are derived in physics. After exploring how and to what extent we might justify such assumptions on methodological grounds or through appeal to speculative future physics, I consider the apparent failure of naturalness in cosmology and in the Standard Model. I argue that any such naturalness failure threatens to undermine the entire structure of our understanding of intertheoretic reduction, and so risks a much larger crisis in physics than is sometimes suggested; I briefly review some currently-popular strategies that might avoid that crisis.

### Spontaneous Symmetry Breaking in Finite Quantum Systems: a decoherent-histories approach (2018)

In submission.

Spontaneous symmetry breaking (SSB) in quantum systems, such as ferromagnets, is normally described as (or as arising from) degeneracy of the ground state; however, it is well established that this degeneracy only occurs in spatially infinite systems, and even better established that ferromagnets are not spatially infinite. I review this well-known paradox, and consider a popular solution where the symmetry is explicitly broken by some external field which goes to zero in the infinite-volume limit; although this is formally satisfactory, I argue that it must be rejected as a physical explanation of SSB since it fails to reproduce some important features of the phenomenology. Motivated by considerations from the analogous classical system, I argue that SSB in finite systems should be understood in terms of the approximate decoupling of the system's state space into dynamically-isolated sectors, related by a symmetry transformation; I use the formalism of decoherent histories to make this more precise and to quantify the effect, showing that it is more than sufficient to explain SSB in realistic systems and that it goes over in a smooth and natural way to the infinite limit.

### The Quantum Theory of Fields (2018)

In E. Knox and A. Wilson (ed.), *'The Routledge Companion to Philosophy of Physics'* (Routledge, 2021).

This is an introduction to quantum field theory and its conceptual and philosophical problems, aimed at non-specialists (but assuming some prior exposure to quantum mechanics).

### Review of "Interpreting Quantum Theories", by Laura Ruetsche (2014)

*British Journal for the Philosophy of Science* 64 (2014), 425-428

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### Taking Particle Physics Seriously: A critique of the algebraic approach to quantum field theory (2011)

*Studies in the History and Philosophy of Modern Physics* 42 (2011) pp.116-125

I argue against the currently-prevalent view in philosophy of physics 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 the position that AQFT and CQFT, understood in an appropriate sense, ought to 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.

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### QFT, Antimatter, and Symmetry (2009)

*Studies in the History and Philosophy of Modern Physics* 40 (2009) 209-222.

A systematic analysis is made of the relations between the symmetries of a classical field and the symmetries of the one-particle quantum system that results from quantizing that field in regimes where interactions are weak. The results are applied to gain a greater insight into the phenomenon of antimatter.

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### In defence of naivete: the conceptual status of Lagrangian QFT (2001)

*Synthese* 151 (2006) 33-80.

I analyse the conceptual and mathematical foundations of Lagrangian quantum field theory (that is, the "naive" quantum field theory used in mainstream physics, as opposed to algebraic quantum field theory). The objective is to see whether Lagrangian quantum field theory 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.

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### Emergence of particles from bosonic quantum field theory (2001)

Unpublished (cite as arxiv.org/pdf/quant-ph/0112149v1)

An examination is made of the way in which particles emerge from linear, bosonic, massive quantum field theories. Two different constructions of the one-particle subspace of such theories are given, both illustrating the importance of the interplay between the quantum-mechanical linear structure and the classical one. Some comments are made on the Newton-Wigner representation of one-particle states, and on the relationship between the approach of this paper and those of Segal, and of Haag and Ruelle.

(Note: this was actually accepted by *Studies in the History and Philosophy of Modern Physics,* pending minor revisions, back in 2003 or so. For various reasons I never got around to making the revisions; by now, I'd probably need to rewrite it quite a lot, since my views have shifted a bit, more in terms of presentation than actual content).