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1. When there are no fermion mass terms, the Dirac part of the Lagrangian posseses an SU(N) left X SU(N) right flavour symmetry for N flavours of fermions. This can be "re-arranged" as an SU(N) vector X SU(N) axial symmetry. The axial part is spontaneously broken by the quark condensate. People often talk about spontaneous breaking of the SU(2) axial symmetry of up and down quarks, and how the pions are the associated goldstone bosons; however, when there are no quark masses in the Lagrangian it actually possessed and SU(6) vector X SU(6) axial symmetry. Why does no one talk about this symmetry, and why dont people study all the mesons as the goldstone bosons of this broken symmetry as they do with broken SU(2) symmetry?

2. Why do people talk about there being an approximate SU(3) flavour symmetry amongst the u,d and s quarks when actually there is a U(3) symmetry? There is no reason why the transformation has to be a special one, the Dirac Lagrangian is invariant under a global unitary transformation.

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# Chiral symmetry breaking and approximate flavour symmetry

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