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Please help me with basic question more I think more I get confused...

In O(n) space there are n(n-1)/2 generators...

suppose I have symmetric tensor in O(n) space, it will have n(n+1)/2 independent components... and i am building invariant potential from it (quartic polynomial expression), then I will find which components minimize my potential and will have symmetry breaking.

Broken generators will transform into Goldstone boson.

So initially i have n(n-1)/2 goldstonic degrees of freedom.

But before i minimize my potential i want to diagonalize my tensor...

Does diagonalization consume goldstonic degrees of freedom/consumes generators?

After diagonalisation shall i have again n(n-1)/2 goldstonic degrees of freedom in my bydget or less ?

thank you

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# Symmetry breaking/ degrees of freedom

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