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Oxford University Press eBooks

Broken Symmetry and Physicists' QFT

Laura Ruetsche

Published Jun 2, 2011• 0 citations
Publisher

Abstract

Chapter 12 argued that quantum statistical mechanics puts unitarily inequivalent representations to use in ways no rigid interpretation can make sense of. Two features of working QFTs which promise a quantum field theoretic realization of Chapter 12's argument are Goldstone bosons and the Higgs mechanism. This chapter explains why they're promising by presenting them as instance of broken symmetry. Then it tempers the promise by admitting that the working QFTs in which these features occur are less mathematically explicit than they need to be to persuasively realize the argument of Chapter 12. The chapter closes by extracting from this very circumstance a non-conclusive reason to lend the argument of Chapter 12 interpretive weight. The reason is that our best theories of physics are still under construction, and their successors could share with the models presented in Chapter 12 the features on which the argument of Chapter 12 hinged.

DOI
10.1093/acprof:oso/9780199535408.003.0014

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Chapter 12 argued that quantum statistical mechanics puts unitarily inequivalent representations to use in ways no rigid interpretation can make sense of. Two features of working QFTs which promise a quantum field theoretic realization of Chapter 12's argument are Goldstone bosons and the Higgs mechanism. This chapter explains why they're promising by presenting them as instance of broken symmetry. Then it tempers the promise by admitting that the working QFTs in which these features occur are less mathematically explicit than they need to be to persuasively realize the argument of Chapter 12. The chapter closes by extracting from this very circumstance a non-conclusive reason to lend the argument of Chapter 12 interpretive weight. The reason is that our best theories of physics are still under construction, and their successors could share with the models presented in Chapter 12 the features on which the argument of Chapter 12 hinged.
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Philosophical analysis of spontaneous symmetry breaking (SSB) in particle physics has been hindered by the unavailability of rigorous formulations of models in quantum field theory (QFT). A strategy for addressing this problem is to use the rigorous models that have been constructed for SSB in quantum statistical mechanics (QSM) systems as a basis for drawing analogous conclusions about SSB in QFT. On the basis of an analysis of this strategy as an instance of the application of the same mathematical formalism to different domains and as an instance of drawing analogies between domains, I conclude that certain structural explanations can be exported from QSM to QFT but that causal explanations cannot.
This chapter considers another route to a particle interpretation of quantum field theory, one mediated by the existence of techniques (such as the use of Feynman diagrams to guide calculation) and explanations (such as the appeal to cosmological particle creation to account for decelerating cosmic expansion) best understood in terms of particles. Looking close at these techniques and explanations, the chapter argues that they rely on the presence of unitarily inequivalent representations, the very presence, Chapters 8 and 9 contended, that frustrates fundamental particle interpretation.
Scientific realism has traditionally maintained that our best scientific theories can be regarded as more or less true and as representing the world as it is (more or less). However, one of our very best current theories—quantum mechanics—has famously resisted such a realist construal, threatening to undermine the realist stance altogether. The chapters in this volume carefully examine this tension and the reasons behind it, including the underdetermination generated by the multiplicity of formulations and interpretations of quantum physics, each presenting a different way the world could be. Authors in this volume offer a range of alternative ways forward: some suggest new articulations of realism, limiting our commitments in one way or another; others attempt to articulate a ‘third way’ between traditional forms of realism and antirealism, or are critical of such attempts. Still others argue that quantum theory itself should be reconceptualised, or at least alternative formulations should be considered in the hope of evading the problems faced by realism. And some examine the nature of these issues when moving beyond quantum mechanics to quantum field theory. Taken together they offer an exciting new set of perspectives on one of the most fundamental questions in the philosophy of modern physics: how can one be a realist about quantum theory, and what does this realism amount to?
Philosophical analysis of spontaneous symmetry breaking (SSB) in particle physics has been hindered by the unavailability of rigorous formulations of models in quantum field theory (QFT). A strategy for addressing this problem is to use the rigorous models that have been constructed for SSB in quantum statistical mechanics (QSM) systems as a basis for drawing analogous conclusions about SSB in QFT. Based on an analysis of this strategy as an instance of the application of the same mathematical formalism to different domains and as an instance of drawing analogies between domains, I conclude that certain structural explanations can be exported from QSM to QFT, but that causal explanations cannot.
The availability of unitarily inequivalent representations of the canonical commutation relations constituting a quantization of a classical field theory raises questions about how to formulate and pursue quantum field theory. In a minimally technical way, I explain how these questions arise and how advocates of the Hilbert space and of the algebraic approaches to quantum theory might answer them. Where these answers differ, I sketch considerations for and against each approach, as well as considerations which might temper their apparent rivalry.