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Given CERN’s announcement today, I wonder what the nPOV about it is. On nLab, ’Higgs’ only appears in Higgs bundle, which, according to Wikipedia, is due to Hitchin
who named the field $\phi$ after Peter Higgs because of an analogy with Higgs bosons.
We have an unfilled Higgs boson entry.
So what do we have? A Higgs bundle is a holomorphic vector bundle together with a Higgs field. And Higgs fields resemble somehow a field which describes the Higgs boson.
There is also the notion of a Higgs field for $\Omega G$ bundles for $G$ a (simply-connected) Lie group, dating back to
H. Garland and M. K. Murray. Kac-Moody monopoles and periodic instantons. Comm. Math. Phys., 120(2):335–351, 1988.
It is used in the article
M. K. Murray and D. Stevenson. Higgs fields, bundle gerbes and string structures. Comm. Math. Phys., 243(3):541–555, 2003. arXiv
in relation to string structures, and carried forward in the work of Murray, Vozzo and collaborators.
Given CERN’s announcement today, I wonder what the nPOV about it is.
Your wondering may be too ambitious. To give a crass analogy: it might be a bit like wondering what the $n$POV is on the fact that the Moon exists.
More in detail: there is no lack of proposals for realizing the Higgs field in various big schemes of mathematical structures modelling physics; and these may have an $n$POV.
For instance
in the technicolor model the Higgs field is not a fundamental particle but a compound of fermions. This realizes the Higgs effect entirely in ordinary gauge theory;
(gauge theory has a beautiful nPOV)
in string theory (see string phenomenology) a Higss can arise in all sorts of ways. Notably in “intersecting brane models” it arises from strings localized at intersecting points (I can’t find a introduction to this aimed at a genuine lay audience, but for a typical kind of survey see for instance around slide 33 here)
(string theory seems to have an even more beautiful nPOV: the above nPOV on gauge theory gives rise to all kinds of string-theoretic structures, but of course this is still “being explored”)
in noncommutative geometry it has been shown that the Higgs may be modeled as a component of the gauge bosons assuming that the KK-reduction is over certain non-commutative space of classical dimension 0.
(again, this takes gauge theory as fundamental, and adds the aspect of non-commutativity).
What will happen next at experiments such as of course the LHC is that people will try to study in detail what exactly it is that they have found at 125 GeV. In principle one imagines that studying this thing closely will reveal what, if any, of the above “models beyond the standard model” give the right description of the Higgs.
Well, I wasn’t expecting a derivation of 125.3GeV from first principles ;)
I’ve added what you wrote above to Higgs field and there’s a stub now for Higgs boson.
Perhaps David R. could disambiguate from the sense he described.
I’ve added
Thanks! Clearly this deserves to be expanded on, but maybe it’s a start.
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