The renormalisation group and effective field theories

Weingard, Robert

doi:10.1007/bf01063904

Cited by 40 publications

(27 citation statements)

References 8 publications

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“…Effective theories have proven to be a powerful tool for the investigation of the physical world; when combined with group theoretic arguments, they have allowed for principled exploration of phenomena where the underlying mechanisms remain unclear or unknown [43]. We have shown here how effective theories can extend to irreversible, dissipative and out-of-equilibrium systems with a demonstration that relates an underlying mechanism (the Boolean circuits) to a higher-level decomposition that permits coarse-graining.…”

Section: Discussionmentioning

confidence: 94%

Effective theories for circuits and automata

DeDeo

2011

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Abstracting an effective theory from a complicated process is central to the study of complexity. Even when the underlying mechanisms are understood, or at least measurable, the presence of dissipation and irreversibility in biological, computational and social systems makes the problem harder. Here we demonstrate the construction of effective theories in the presence of both irreversibility and noise, in a dynamical model with underlying feedback. We use the Krohn-Rhodes theorem to show how the composition of underlying mechanisms can lead to innovations in the emergent effective theory. We show how dissipation and irreversibility fundamentally limit the lifetimes of these emergent structures, even though, on short timescales, the group properties may be enriched compared to their noiseless counterparts. Many systems, especially those with large numbers of underlying degrees of freedom, are best described by what are known as effective theories. These theories allow us to describe the relevant high-level phenomena while remaining ignorant, or at least agnostic, about the fine-grained details of a system's state. Here, we show how to construct effective theories of phenomena that may show irreversibility or dissipation, a question particularly relevant for biological, social and computational systems. We use a hierarchical decomposition technique from semigroup theory that allows one to take finite state automata (standard, if restricted, models of computation) and determine the irreducible components of the process. Truncating the hierarchy provides an effective theory. We study how different underlying mechanisms lead to qualitatively different effective theories, and show how noise and irreversibility interact to produce new computational phenomena on short timescales, which, in the presence of irreversibility, eventually dissipate at longer intervals.

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Section: Discussionmentioning

confidence: 94%

Effective theories for circuits and automata

DeDeo

2011

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…3 There are, of course, exceptions. Teller ([1989], [1995]) and Huggett and Weingard ([1995]) examine perturbative renormalization from a philosophical perspective. There has also been discussion of virtual particles (Weingard [1988]; Redhead [1988]) and Feynman diagrams (Meynel, 2008;Wüthrich, 2012) in the philosophical literature, which engages with QFT perturbation theory.…”

Section: Three Worries About Perturbative Quantum Field Theorymentioning

confidence: 99%

The Real Problem with Perturbative Quantum Field Theory

Fraser¹

2020

The British Journal for the Philosophy of Science

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The perturbative approach to quantum field theory (QFT) has long been viewed with suspicion by philosophers of science. This paper offers a diagnosis of its conceptual problems. Drawing on Norton's ([2012]) discussion of the notion of approximation I argue that perturbative QFT ought to be understood as producing approximations without specifying an underlying QFT model. This analysis leads to a reassessment of common worries about perturbative QFT. What ends up being the key issue with the approach on this picture is not mathematical rigour, or the threat of inconsistency, but the need for a physical explanation of its empirical success.

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“…What makes the proposal of Cao and Schweber particularly ambitious is that in addition to the hierarchal picture of nature just described, they also conclude that EFTs "support a pluralism in theoretical ontology, an antifoundationalism in epistemology and an antireductionism in methodology" (p.69). I will return briefly to this more extreme claim when discussing the criticism of [32], but for the moment I simply endorse the conclusion of [33] that this constitutes a significant overreach and is not at all entailed by the success of the effective field theory approach. However, one need not subscribe wholesale to Cao and Schweber's conclusions in order to hold onto the belief that an ontology of quasi-autonomous domains is licensed by the Decoupling Theorem.…”

Section: A Uniform Notion Of Naturalnessmentioning

confidence: 99%

“…32 For an excellent review, see [13]. 33 Of particular relevance here, the GIM mechanism banishes so-called flavor-changing neutral currents (FCNC) from the theory. The presence of these currents implied that certain kaon decay processes, such as k → µµ, should occur at rates much higher than experimentally observed.…”

Section: A Uniform Notion Of Naturalnessmentioning

confidence: 99%

Naturalness, the autonomy of scales, and the 125GeV Higgs

Williams

2015

Studies in History and Philosophy of Science Part B: Studies in

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The recent discovery of the Higgs at 125 GeV by the ATLAS and CMS experiments at the LHC has put significant pressure on a principle which has guided much theorizing in high energy physics over the last 40 years, the principle of naturalness. In this paper, I provide an explication of the conceptual foundations and physical significance of the naturalness principle. I argue that the naturalness principle is well-grounded both empirically and in the theoretical structure of effective field theories, and that it was reasonable for physicists to endorse it. Its possible failure to be realized in nature, as suggested by recent LHC data, thus represents an empirical challenge to certain foundational aspects of our understanding of QFT. In particular, I argue that its failure would undermine one class of recent proposals which claim that QFT provides us with a picture of the world as being structured into quasi-autonomous physical domains.

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The renormalisation group and effective field theories

Cited by 40 publications

References 8 publications

Effective theories for circuits and automata

Effective theories for circuits and automata

The Real Problem with Perturbative Quantum Field Theory

Naturalness, the autonomy of scales, and the 125GeV Higgs

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