Logarithmic representations of the conformal Galilean algebra (CGA) and the Exotic Conformal Galilean algebra ({sc ecga}) are constructed. This can be achieved by non-decomposable representations of the scaling dimensions or the rapidity indices, spe
cific to conformal galilean algebras. Logarithmic representations of the non-exotic CGA lead to the expected constraints on scaling dimensions and rapidities and also on the logarithmic contributions in the co-variant two-point functions. On the other hand, the {sc ecga} admits several distinct situations which are distinguished by different sets of constraints and distinct scaling forms of the two-point functions. Two distinct realisations for the spatial rotations are identified as well. The first example of a reducible, but non-decomposable representation, without logarithmic terms in the two-point function is given.
We show how logarithmic terms may arise in the correlators of fields which belong to the representation of the Schrodinger-Virasoro algebra (SV) or the affine Galilean Conformal Algebra (GCA). We show that in GCA, only scaling operator can have a Jor
danian form and rapidity can not. We observe that in both algebras logarithmic dependence appears along the time direction alone.
