  We study the transversely metaplectic structure and the transversely
symplectic Dirac operator on a transversely symplectic foliation. Moreover, we
give the Weitzenbock type formula for transversely symplectic Dirac operators
and we estimate the lower bound of the eigenvalues of the transversely
symplectic Dirac operator on special spinors space on transverse Kahler
foliations.
