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In explicit symmetry breaking, the equations of motion of a physical system are variant under the broken symmetry; by contrast, for spontaneous symmetry breaking (SSB), these equations are invariant, but the entire system is not because its vacuum (background) is non-invariant. Further use for the SSB characteristic nonlinear realizations (Goldstone mode), and the group theoretical patterns involved.
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Spontaneous symmetry breaking in fluids
BACKGROUND:
One can think of solids as spontaneously breaking translational symmetries in the sense that each atom in a lattice has to pick a particular position. Yet, as with everything in our unive …
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Goldstone theorem in Weinberg vol 2
I was reading the proof of Goldstone's theorem (the operator proof starting on page 170) in Weinberg's book on QFT (Volume II) and got confused. I am able to follow each line of the proof, but as a wh …
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Coset construction for Goldstones in Weinberg Vol II
In section 19.6 of Weinberg Vol II, there is a discussion of the coset construction for effective actions of Goldstones arising from spontaneous symmetry breaking of internal symmetries. In this secti …
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Non-abelian Goldstone bosons
Suppose we have a theory with a non-abelian symmetry group $G$ that is spontaneously broken to the subgroup $H\subset G$--this is a global symmetry, $not$ a gauge redundancy. Let $X^a$ be the generato …
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Fermi liquid/gas and Goldstones
Often, we say that the low-energy excitations of a quantum system that spontaneously breaks certain symmetries is described by Goldstone bosons. It is also well-known that Fermi liquids and gases are …