  We propose a generalization of the momentum map on a symplectic manifold with
a Lie algebra action to a Courant algebroid structure. The theory of a momentum
section on a Lie algebroid is generalized to the theory compatible with a
Courant algebroid. As an example, we identify the momentum section in a
constrained Hamiltonian mechanics with Courant algebroid symmetry. Moreover, we
construct cohomological formulations by considering the BFV and BV formalism of
this Hamiltonian system. The Weil algebra for this structure is constructed.
