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A Philosophical Look at the Higgs Mechanism

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Abstract

On the occasion of the recent experimental detection of a Higgs-type particle at the Large Hadron Collider at CERN, the paper reviews philosophical aspects of the Higgs mechanism as the presently preferred account of the generation of particle masses in the Standard Model of elementary particle physics and its most discussed extensions. The paper serves a twofold purpose: on the one hand, it offers an introduction to the Higgs mechanism and its most interesting philosophical aspects to readers not familiar with it; on the other hand, it clarifies widespread misunderstandings related to the role of gauge symmetries and their breaking in it.

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Notes

  1. See, for instance, Earman (2004, section 6), and Struyve (2011, section 7), for more detailed discussions of this point, which are aimed at philosophers.

  2. The standard view of gauge symmetries as non-empirical is attacked by Maudlin (1998) in terms of considerations on the Aharonov–Bohm effect, a direct response by Healey defending the standard view can be found in Healey (1998); a more recent defence of the standard view of gauge symmetries as non-empirical and a careful assessment of its philosophical ramifications can be found in Healey (2007) and Healey (2009). For a recent criticism of the standard perspective on local gauge symmetries as in all circumstances non-empirical see Greaves and Wallace (2014), for a critical response see Friederich (2014).

  3. See, for instance, Weinberg (1974).

  4. For further interesting considerations on the prospects of structural realist readings of gauge symmetries see Roberts (2011).

  5. See Chapter 11.9 of Jackson (1998) for a canonical textbook introduction to the relativistic formulation of electromagnetism, where the tensor \(F_{\mu \nu }\) is introduced and its properties are discussed in great detail.

  6. The historically most significant contributions to the original development of the Higgs mechanism include Anderson (1963); Englert and Brout (1964); Higgs (1964); Guralnik et al. (1964); Kibble (1967). See Karaca (2013) for a recent critical study of the historical origins of the Higgs mechanism and the electroweak theory.

  7. Strocchi (2008) gives a comprehensive and conceptually rigorous introduction to spontaneous symmetry breaking, which makes all of the notions employed here mathematically precise.

  8. For accessible introductions to this topic see Ruetsche (2011), Chapter 13, and (Strocchi 2008), Part II.

  9. Elitzur proved the theorem for the case of a Higgs field with fixed modulus, see Elitzur (1975). The result was generalised to the case of a Higgs field with variable modulus by De Angelis et al. (1978).

  10. More precisely, the theorem states that the expectation value of any monomial which transforms as a non-trivial irreducible representation of the local gauge group must vanish. I would like to thank an anonymous referee of this journal for proposing this concise formulation.

  11. See the proof sketches of Elitzur’s theorem Strocchi (1985, chapter II 2.5), and Fröhlich et al. (1981, section 3) for more details. For a more rigorous textbook version applied to the special case of the vacuum expectation value of the Higgs field see Itzykson and Drouffe (1989, chapter 6.1.3).

  12. For more detailed discussions, see Friederich (2013) and Caudy and Greensite (2008). The results presented in the latter paper provide the basis for the main claims made in what follows.

  13. At first glance, the spontaneous breaking of remnant global symmetries may seem astonishing in the light of Elitzur’s theorem, since global symmetry transformations are special cases of local symmetry transformations, and local gauge symmetries cannot break spontaneously, as Elitzur’s theorem assures us. The puzzle is resolved by noting that the global symmetries are potentially broken only in the gauge fixed theory, where local gauge symmetry is no longer present. One should note, however, that results about remnant gauge symmetry breaking can be recovered by lattice calculations without gauge fixing in a more indirect manner as well, which means that, from a methodological point of view, gauge fixing is not the only option to determine remnant global gauge symmetry breaking.

  14. See Caudy and Greensite (2008) for a detailed elaboration and defence of these claims, based on detailed numerical investigations as well as on an earlier rigorous results by Fradkin and Shenker (1979).

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Acknowledgments

I would like to thank Jeremy Butterfield, Friedrich Harbach, Koray Karaca and two anonymous referees for many helpful comments on earlier versions of this paper. Work on the topics discussed here was carried out in the project “An ontological and epistemological analysis of the Higgs-mechanism” at Wuppertal University, funded by Deutsche Forschungsgemeinschaft (DFG, contract HA 2990/4-1).

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    Simon Friederich

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Friederich, S. A Philosophical Look at the Higgs Mechanism. J Gen Philos Sci 45, 335–350 (2014). https://doi.org/10.1007/s10838-014-9257-5

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