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In this Lubos says that Higgs VEV is also called vacuum Higgs condensate which the term used by Prof. Englert in this video. Since the Higgs field is bosonic, I wonder whether this terminology has anything to do with Bose-Einstein condensate or condensation (which occurs in a dilute gas of bosons very close to absolute zero). This answer too by Maimon suggested something similar. Can one explain the similarity and connection of BE condensate and the VEV of Higgs?

Does it mean that the electroweak phase transition is related to the BE condensation of the Higgs field?

A similar question was previously asked here.

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  • $\begingroup$ There may be large temperatures for the bose-condensation. For example, the superconductivity, whose origin is similar to the bose-consensation (of the cooper pairs), may arise for high temperatures. $\endgroup$ – Name YYY Dec 31 '16 at 18:08
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    $\begingroup$ In this context the condensate is simply the vacuum state of a quantum field. It applies to any field whether the field is bosonic or not. However for all fields the VEV is a Lorentz scalar. $\endgroup$ – John Rennie Jan 1 '17 at 9:33
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You learned in school that condensation is a gas or vapour cooling to form a liquid, an example of what physicists call a phase transition. Field theory and particle physics use "condensation" to refer to energy-lowering phase transitions, but that's all BEC and Higgs condensation have in common. In BEC, particles' mutual state is determined by energy minimisation. In Higgs condensation, energy minimisation determines the amplitude but not phase of the Higgs field, and the amplitude is nonzero. This signifies two things, spontaneous symmetry breaking and tachyon condensation. The Higgs potential may be written as $V=-M^2|\phi|^2+\frac{\lambda}{2}|\phi|^4$. The term "tachyon" reflects the negative quadratic term coefficient, but the term is misleading because after quantization no tachyons (particles of negative squared mass) result because $\frac{\partial^2 V}{\partial \phi \partial \phi^\ast}$ lacks negative eigenvalues.

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  • $\begingroup$ I believe there's actually a lot more connection. Many BEC processes in condensed matter physics, when written in field theory form, are the same as the Higgs mechanism. $\endgroup$ – Chenfeng Nov 15 '17 at 7:28
  • $\begingroup$ @Chenfeng As in they still have a Mexican hat potential? That's unsurprising if the same consequences are to result. $\endgroup$ – J.G. Nov 15 '17 at 9:35
  • $\begingroup$ Not necessarily a Mexican hat but almost always a spontaneous symmetry breaking (including the prototypical weakly-interacting Bose gas), which is considered the essence of the Higgs mechanism (in condensed matter physics at least). Although there might be a language mismatch, as people in condensed matter physics might not always think of the SM Higgs when they talk about the Higgs mechanism, rather some of them may think of SM Higgs as just a special case. $\endgroup$ – Chenfeng Nov 16 '17 at 11:53
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I think VEV and condensate terms are quite similar. BEC condensate is just about particles but Higgs VEV is about fields, but they are all about setting to the lowest energy possible for the system. You can see BEC condensate but VEV of fields are much more indirect.

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