Sigma Club Seminar by Alexander Niederklapfer (LSE Philosophy)

Title: Localisation of Particles in Quantum Field theory

Abstract: The consensus in philosophy of physics is that quantum field theories (QFTs) are, at the fundamental level, not about particles. Nevertheless, much of the relevant empirical data is gathered from particle detectors. Reconciling this particle phenomenology with the underlying field-theoretic framework therefore remains an important task in the interpretation of QFTs. In this talk I will present and defend a philosophically under-explored approach due to Haag and collaborators that aims to define particles in an operational manner and compare it to a more realist approach based on Wallace's (2006) proposal of “effective localisation''. Overall, I conclude that Haag's approach leads to the most satisfactory notion of particles currently available.

A central challenge for particle notions is localizability: several no-go theorems show that there cannot be strictly localised states in QFTs, yet experiments are still described in terms of locally detected particles. An important result is the Reeh-Schlieder theorem, which prohibits non-trivial, strictly localised observables with zero vacuum response -- a desirable combination for operators describing properties of localised particles. I contrast two approaches to overcome these implications by each relaxing one of the desiderata of zero vacuum response and strict locality; on the one hand Wallace’s “effective localisation”, and on the other hand, what I will call “almost localisation”, based on Haag’s notion of almost local operators. I discuss to what extent they can lead to particle pictures that satisfy three desiderata: (i) incorporating a notion of localisation, (ii) being able to describe how particles arise from interacting theories via scattering theory, and (iii) applying as broadly as possible, including to theories involving electrically charged particles. By comparing the two approaches I clarify both the similarities they share (explicating Wallace's claim that Haag-Ruelle scattering theory is “essentially the same framework'' (2001, p. 38)) and, more importantly, the aspects in which they differ. I argue that the two approaches not only correspond to different ways of addressing the constraints posed by the Reeh-Schlieder theorem, but that they also implement different strategies characterising localisation. I conclude that while a minimal operational reading can accommodate both approaches, Haag's leads to a more powerful particle picture overall and should thus be preferred.

This event will take place in person on LSE’s campus. However, those unable to attend in person will have the option of taking part online.

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