thanks for the reply.
I think my question might actually be simpler than you are suspecting. I'm happy with why we're allowed to make these global changes by the freedom to make redefinitions in the fields. My question really could have been stated as just a mathematical one (without even mentioning CKM or the SM), about how we can take some arbitrary 3x3 unitrary matrix, apply some phase factors to it to obtain
[tex]\mathrm{e}^{i\beta_i}U_{ij} \mathrm{e}^{+i\alpha_j} [/tex]
to make the first row and column real, and eliminate 5 of the 9 real parameters needed to specify 3x3 unitary matrix. Is there some conventional parametrisation that one writes an arbitrary 3x3 unitary matrix in terms of the 9 needed parameters, for which this then becomes obvious?
