A note on the quadrupole (N->Δ) transition amplitude in quark models

Due to the usual strong truncation of the basis in dynamical quark model calculations, the charge-current operator for the quadrupole (N -> Δ) transition violates gauge invariance. It is demonstrated explicitly for the nonrelativistic constituent quark model that, in the standard 2 (h/2π)ω-basis, calculations of the quadrupole transition form factor differ by an order of magnitude, depending on whether one uses the charge or current for the evaluation. Since this effect is related to the behaviour of the two operators under hermitean conjugation and time reversal, it is expected to be of importance also for other wavefunctions as well as in relativistic models. (orig.)