Abstract
An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super Dirac systems. Under the obtained symmetry constraint, the
n
-th flow of the super Dirac hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold
R
4
N
|2
N
with the corresponding dynamical variables
x
and
t
n
. The integrals of motion required for Liouville integrability are explicitly given.