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When a theory is symmetric with respect to a symmetry group, but requires that one element of the group be distinct, then spontaneous symmetry breaking has occurred. The theory must not dictate which member is distinct, only that one is. From this point on, the theory can be treated as if this element actually is distinct, with the proviso that any results found in this way must be resymmetrized, by taking the average of each of the elements of the group being the distinct one.

The crucial concept in physics theories is the order parameter. If there is a field (often a background field) which acquires an expectation value (not necessarily a vacuum expectation value) which is not invariant under the symmetry in question, we say that the system is in the ordered phase, and the symmetry is spontaneously broken. This is because other subsystems interact with the order parameter which forms a "frame of reference" to be measured against, so to speak. In that case, the vacuum state does not obey the initial symmetry (which would put it in the Wigner mode), and, instead has the (hidden) symmetry implemented in the Nambu–Goldstone mode. Normally, in the absence of the Higgs mechanism, massless Goldstone bosons arise.
 
When a theory is symmetric with respect to a symmetry group, but requires that one element of the group be distinct, then spontaneous symmetry breaking has occurred. The theory must not dictate which member is distinct, only that one is. From this point on, the theory can be treated as if this element actually is distinct, with the proviso that any results found in this way must be resymmetrized, by taking the average of each of the elements of the group being the distinct one.

The crucial concept in physics theories is the order parameter. If there is a field (often a background field) which acquires an expectation value (not necessarily a vacuum expectation value) which is not invariant under the symmetry in question, we say that the system is in the ordered phase, and the symmetry is spontaneously broken. This is because other subsystems interact with the order parameter which forms a "frame of reference" to be measured against, so to speak. In that case, the vacuum state does not obey the initial symmetry (which would put it in the Wigner mode), and, instead has the (hidden) symmetry implemented in the Nambu–Goldstone mode. Normally, in the absence of the Higgs mechanism, massless Goldstone bosons arise.

Oh, you beat me to it. I was just about to say that. :lmao:
 
It's the Battle of the Blues tonight. Duke at UNC. GO HEELS!!!!!
 
mishele said:
^^^^If you are being serious, when and where?

Oh yea I'm serious :D

We leave on the 18th and heading to the island of Kauai and staying in the town of Hanalei on the north shore for a whole 2 weeks. Can't wait
OMG, I was just there last March!!! Amazing island!!! If you have any questions send me a PM!!
Are you planning on doing much hiking?!! I'm so jealous!!!

I had a one night stand w/ o hey tyler....just sayin.
Remember that one amazing night?! lol
 
Purple. My last art teacher made us say "VI-O-LET", but I said "purple" when she wasn't listening.
 
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