Take the tour ×  In a gauge theory (non-abelian for this
question), I am told that two states $|\psi\rangle$ and
$|\phi\rangle$ are to be identified if they are related by a
gauge transformation $U(x)$   But means that two states are to
be identified when the gauge transformation is homogenous, i.e.
independent of $x$.  Does this formally mean that for the one-
particle quark state, the red quark $|1_\text{Red}\rangle$,
green quark $|1_\text{Green}\rangle$, and blue quark
$|1_\text{Blue}\rangle$ are all identified as a single state, as
they are all related by gauge transformations? I would say
yes...  So then I ask, does this mean we are overcounting the
number of color states when we calculate the color-averaged
scattering amplitude? I want to say, no because there are many
quarks in this world, and the color orientation of the incoming
and outgoing quarks with respect to some other colored quark
elsewhere is gauge-invariant....  Is this correct reasoning or
poor thinking?  share|improve this question add com