(adsbygoogle = window.adsbygoogle || []).push({}); The part I understand:

I understand that the spontaneous symmetry breaking of the Higgs produces the 'Mexican hat' potential, with two non-zero stable equilibria.

I understand that as the Higgs is a complex field, there exists a phase component of the field. Under gauge transformations of this Higgs potential (in particular the rotation: [itex]\phi \rightarrow \phi_0 e^{i \theta}[/itex]), you are simply moving between the degenerate ground state of this potential, where this motion simply generates the massless Goldstone bosons, and hence the potential is gauge invariant.

The part I do not understand:

You must now fix the gauge by using a condensate, such that the rotations are gaugevariantas "you want the Higgs to take a specific value". I don't understand what you must fix the gauge. As the ground states are all degenerate, surely the Higgs already has a specific value?

Please do not use the Lagrangian to explain it! Thank you in advance!

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# Why must the Higgs' gauge symmetry be broken?

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