Does the Higgs Mechanism Exist?

Abstract

This paper explores the argument structure of the concept of spontaneous symmetry breaking in the electroweak gauge theory of the Standard Model: the so‐called Higgs mechanism. As commonly understood, the Higgs argument is designed to introduce the masses of the gauge bosons by a spontaneous breaking of the gauge symmetry of an additional field, the Higgs field. The technical derivation of the Higgs mechanism, however, consists in a mere reshuffling of degrees of freedom by transforming the Higgs Lagrangian in a gauge‐invariant manner. This already raises serious doubts about the adequacy of the entire manoeuvre. It will be shown that no straightforward ontic interpretation of the Higgs mechanism is tenable, since gauge transformations possess no real instantiations. In addition, the explanatory value of the Higgs argument will be critically examined.

Acknowledgements

I am deeply grateful to Tim Mexner‐Eynck especially for helping me with some technical details of the present paper, but, what is more, for years of a unique collaboration between philosophy of science and theoretical physics. Many thanks also to Gernot Münster, Wolfgang Unger, and two anonymous referees for useful remarks.

Notes

[1] Of course this well‐known recipe does not entail the existence of a non‐zero interaction field (compare note 6). The logic of the gauge argument has been unfolded by several authors in recent years; see Brown (1999), Lyre (2001), and Martin (2002).

[2] A reaction to Earman certainly worth reading and tentatively in spirit with the present paper, though not as decisive as we are concerning ontological consequences, is Smeenk (2006). Chris Smeenk and I wrote our papers independently and only discovered certain similarities in our views after a recent meeting at a conference.

[3] The original source is Curie (1894); for a systematic discussion of the status of Curie’s principle see for instance Chalmers (1970). In a recent paper, Earman (2004a) addresses the principle’s connections to QFT—thereby repeating his worries about the Higgs mechanism, as already expressed in his quote in the introduction.

[4] It is not necessary to delve into any sophisticated philosophical debate about realism here. We simply use a minimal and, perhaps, commonsensical notion of physical reality, where physical quantities are considered to be connected with observable consequences—and we take this notion, for the purpose of this discussion, as an unproblematic notion.

[5] One might, perhaps, speculate about the introduction of new physical principles here—for instance a new variant of the ‘Cosmic Censorship’, where Nature forever hides imaginary masses from our eyes. But nothing like that has been worked out by anyone yet.

[6] From all the above, the logic of the gauge principle should also become clear: the demand of local gauge invariance prompts the introduction of a covariant derivative D_µ = Û∂_µÛ ⁺. In the usual textbook presentations (e.g. Halzen and Martin 1984, 316), however, the gradient of the phase is written in terms of a vector field, where also the dimensions of a charge come in: ∂_µΞ(x) = −qA_µ (x). This suggests a reading of the covariant derivative D_µ = ∂_µ + iqA_µ (x) as if the existence of a gauge potential A_µ were enforced. But one must be aware of the fact that a thus‐introduced potential is, in fibre bundle terminology, a flat connection only. That is to say, the physically significant curvature tensor, the derivative of the connection, is still zero. Whether, in fact, a particular curvature or gauge field interaction tensor is non‐zero and is as such realized by nature is of course an empirical input and cannot be dictated by demanding local gauge invariance (see note 1 and references therein).

[7] A further note of clarification: the reader might perhaps be puzzled by our claims about the equivalence of the three Lagrangians, on the one hand, and the impossibility of a direct realistic interpretation of ℒ′ as opposed to ℒ‴, on the other hand. There seems to be a tension between our first and third observation in the beginning of section 3. And indeed, observation three hinges on stressing a ‘quick and literal’ interpretation of the particle content of a Lagrangian by simply looking at the mass terms. On the basis of our analysis we may now of course say that such a quick and literal interpretation of ℒ′ cannot directly be gained, but is rather indirectly revealed by the direct interpretation of ℒ‴.