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touqra
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How does symmetry breaking occur?
What does it mean to be an "equivalent" solution. Does it just mean that both S and T are members of some solution set with no preference of selecting one over the other?vanesch said:... when you take a symmetry operation g in G, then g S = T and T is an "equivalent" solution.
I'm a little confused by the term "solution." What are we solving?vanesch said:Now, it can be that for some reason, we have to choose ONE SINGLE solution. Imagine it is a solution from S0. In that case, we have to choose a specific point O, and the solution we take is {O,O}.
How is that? If we translate the origin, the distance between the points is still zero, isn't it?vanesch said:Everything we will do with this particular solution HAS BROKEN THE TRANSLATION SYMMETRY of the problem.
turin said:1) I'm a little confused by the term "solution." What are we solving?
2) How is that? If we translate the origin, the distance between the points is still zero, isn't it?
3) Can you give a more physical example? I am lost in the abstraction.
turin said:So is there always this effective reduction in (non-trivial) degrees of freedom in the problem when symmetry breaking is induced?