  The isoscalar monopole(ISM) and dipole(ISD) excitations in $^{12}$C are
theoretically investigated with the shifted antisymmetrized molecular
dynamics(AMD) plus $3\alpha$-cluster generator coordinate method(GCM). The
small amplitude vibration modes are described by coherent one-particle one-hole
excitations expressed by small shift of single-nucleon Gaussian wave functions
within the AMD framework, whereas the large amplitude cluster modes are
incorporated by superposing $3\alpha$-cluster wave functions in the GCM. The
coupling of the excitations in the intrinsic frame with the rotation and parity
transformation is taken into account microscopically by the angular-momentum
and parity projections. The present calculation describes the ISM and ISD
excitations in a wide energy region covering cluster modes in the low-energy
region and the giant resonances in the high-energy region, though the
quantitative description of the high-energy part is not satisfactory. The
low-energy ISM and ISD strengths of the cluster modes are enhanced by the
radial motion of $\alpha$ clusters, and they split into a couple of states
because of the angular motion of $\alpha$ clusters. The low-energy ISM
strengths exhaust 26% of the EWSR, which is consistent with the experimental
data for the $^{12}$C($0^+_2$;7.65 MeV) and $^{12}$C($0^+_3$;10.3 MeV) measured
by $(e,e')$, $(\alpha,\alpha')$, and ($^6$Li,$^6$Li$'$) scatterings. In the
calculated low-energy ISD strengths, two $1^-$ states (the $1^-_1$ and $1^-_2$)
with the significant strengths are obtained in $E=10-15$ MeV. It is indicated
that the ISD excitations can be a good probe to experimentally search for new
cluster states such as the $^{12}$C($1^-_2$) obtained in the present
calculation.
