  We employ the effective field theory approach for multi-field inflation which
is a generalization of Weinberg's work. In this method the first correction
terms in addition to standard terms in the Lagrangian have been considered.
These terms contain up to the fourth derivative of the fields including the
scalar field and the metric. The results show the possible shapes of the
interaction terms resulting eventually in non-Gaussianity in a general
formalism. In addition generally the speed of sound is different but almost
unity. Since in this method the adiabatic mode is not discriminated initially
so we define the adiabatic as well as entropy modes for a specific two-field
model. It has been shown that the non-Gaussianity of the adiabatic mode and the
entropy mode are correlated in shape and amplitude. It is shown that even for
speed close to unity large non-Gaussianities are possible in multi-field case.
The amount of the non-Gaussianity depends on the curvature of the classical
path in the phase-space in the Hubble unit such that it is large for the large
curvature. In addition it is emphasized that the time derivative of adiabatic
and entropy perturbations do not transform due to the shift symmetry as well as
the original perturbations. Though two specific combinations of them are
invariant under such a symmetry and these combinations should be employed to
construct an effective field theory of multi-field inflation.
