- #1
Neitrino
- 137
- 0
Dear PF...
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
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