What is this symmetry breaking process I keep hearing about?
A quick google and one gets this:http://plato.stanford.edu/entries/symmetry-breaking/
If this does not answer your question?..then your asking the wrong one.
A spontaineous google gets you this:http://www.historyoftheuniverse.com/ssb.html
Thanks for that link, a good summary without getting technical.
I'm particularly interested in symmetries that are broken to produce mass. I think this involves the "Higgs mechanism", but I'm not sure.
Have symmetries principles been reduced to topological properties of spacetime?
Or would topological properties that apply everywhere except at a certain "boundary" qualify as a symmetry breaking principle?
The Anderson-Higgs mechanism does indeed involve spontaneously broken symmetry.
The gist of it is, in the elementary Higgs lagrangian, there is a spontaneously broken SO(2) rotational symmetry that goes into a U(1) local guage symmetry. The thing is there is a strange mixing guage term that doesn't seem to go away in the original lagrangian, but under the symmetry breaking condition it couples to the Goldstone boson term.. The guage field is then said to have acquired mass.
With a clever choice of guage fixing, the original lagrangian, perturbed around the newly inspired ground state now has a massive field.
I wouldn't necessarily call it a topological event *abus de language* perse, its just that the naive form of the potential term contains false vacuum parts, local minima that are not necessarily global. Think of the usual mexican hat potential.
That sort of simplistic example motivates the actual SDM Higgs theories, though the actual nature of the higgs is not known since it has never been observed. Usually in those simple theories, its taken to be a scalar field. In more complicated theories, it can be different (though the remnants often ends up looking like the simple theory + other stuff).
I'd like to quote from ranyart's second link: "After a time the Higgs fields started to decay, to change from zero to non-zero values. This is called spontaneous symmetry breaking. Bubbles of true vacuum (that is, totally empty regions) appeared inside the false vacuum of the Macrocosmos as the symmetry of the fields was spontaneously broken. Within each bubble the Higgs fields spontaneously took on unpredictable values. Inflation continued for a while within each bubble as it moved from the false to the true vacuum."
"true vacuum,... false vacuum"... intriguing. "bubbles of true vacuum" certainly sounds like "space tearing" and forming some sort of boundary to normal space that is then interpreted as resulting in mass, does it not? Is there any mention made about a possible connection between the Higgs mechanism and space tearing? I don't remember where I heard about space tearing, but it was back in the mid to late 80's, if I recall.
My second question was whether it was an abuse of language to call some topological property that applies to all of normal space (the false vacuum) but does not apply for the true vacuum. Is symmetry broken at the boundary between them. I'm thinking of points in normal space being elements of an open neighborhood, but points on the boundary being elements of a half open set. I think that's the verbage for this.
Comments welcome. Thanks.
Firstly if I make any comments it will be my personal understanding, and as I am un-qualified I will refrain from doing so.
What I will tell you that you need to go google and Xarchive some of Andre Linde's papers, he has is own theory of course, but has slightly more Qualifications than I
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