  The multipole amplitudes for the N - Delta electromagnetic transition are
computed in the framework of the linear sigma model and the chiral
chromodielectric model for small and moderate photon virtualities. The models
include quark and meson degrees of freedom and the nucleon and the delta are
clusters of three valence hedgehog quarks surrounded by meson clouds described
by coherent states. Angular momentum and isospin projections are performed to
endow model states representing the nucleon and the delta with proper quantum
numbers. Recoil corrections involved in the process $\gamma_{\rm v} N \to
\Delta$ are taken into account by performing linear momentum projection of the
initial and final baryon states. The ratios $E2/M1$ and $C2/M1$ are in good
agreement with the data in the two models, but the magnetic amplitude is better
reproduced in the Linear Sigma Model. The ratios show little dependence with
the model parameters. Both in the Linear Sigma Model and in the
Chromodielectric Model the charged pions are responsible for the non-vanishing
quadrupole-electric and -coulomb amplitudes. The recoil corrections enhance the
results obtained for the amplitudes without linear momentum projection,
improving the comparison with experimental data. The dependence of the
theoretical amplitudes with the choice of the reference frame is also studied.
